Cho x; y; z khác ± 1 và xy + yz + xz = 1. Chọn câu đúng?

A. $\frac{\text{x}}{\text{1}-{\text{x}}^{\text{2}}}+\frac{\text{y}}{\text{1}-{\text{y}}^{\text{2}}}+\frac{\text{z}}{\text{1}-{\text{z}}^{\text{2}}}=\frac{\text{xyz}}{\text{(1}-{\text{x}}^{\text{2}}\text{)(1}-{\text{y}}^{\text{2}}\text{)(1}-{\text{z}}^{\text{2}}\text{)}}$

B. $\frac{\text{x}}{\text{1}-{\text{x}}^{\text{2}}}+\frac{\text{y}}{\text{1}-{\text{y}}^{\text{2}}}+\frac{\text{z}}{\text{1}-{\text{z}}^{\text{2}}}=\frac{\text{3xyz}}{\text{(1}-{\text{x}}^{\text{2}}\text{)(1}-{\text{y}}^{\text{2}}\text{)(1}-{\text{z}}^{\text{2}}\text{)}}$

C. $\frac{\text{x}}{\text{1}-{\text{x}}^{\text{2}}}+\frac{\text{y}}{\text{1}-{\text{y}}^{\text{2}}}+\frac{\text{z}}{\text{1}-{\text{z}}^{\text{2}}}=\frac{\text{4xyz}}{\text{(1}-{\text{x}}^{\text{2}}\text{)(1}-{\text{y}}^{\text{2}}\text{)(1}-{\text{z}}^{\text{2}}\text{)}}$

D. $\frac{\text{x}}{\text{1}-{\text{x}}^{\text{2}}}+\frac{\text{y}}{\text{1}-{\text{y}}^{\text{2}}}+\frac{\text{z}}{\text{1}-{\text{z}}^{\text{2}}}=\frac{\text{xyz(x}+\text{y}+\text{z)}}{\text{(1}-{\text{x}}^{\text{2}}\text{)(1}-{\text{y}}^{\text{2}}\text{)(1}-{\text{z}}^{\text{2}}\text{)}}$

Cho a, b, c thỏa mãn abc = 2017. Tính giá trị biểu thức sau $Q = \frac{\text{2017a}}{\text{ab}+\text{2017a}+\text{2017}}+\frac{\text{b}}{\text{bc}+\text{b}+\text{2017}}+\frac{\text{c}}{\text{ac}+\text{1}+\text{c}}$

A. Q = -1

B. Q = 0

C. Q = 2

D. Q = 1

Tìm P biết: P + $\frac{\text{4x}-\text{12}}{{\text{x}}^{\text{3}}-{\text{3x}}^{\text{2}}-\text{4x}+\text{12}}=\frac{\text{3}}{\text{x}-\text{3}}-\frac{{\text{x}}^{\text{2}}}{\text{4}-{\text{x}}^{\text{2}}}$

A. $P = \frac{\text{x}}{\text{x}+\text{3}}$

B. $P = \frac{\text{x}}{\text{x}-\text{3}}$

C. $P = \frac{\text{1}}{\text{x}-\text{3}}$

D. $P = \frac{\text{x-3}}{\text{x}}$

Tìm P biết $\frac{\text{x}-\text{1}}{{\text{x}}^{\text{2}}-\text{x}+\text{1}}-\text{P}=\frac{\text{2}}{\text{x}-\text{1}}+\frac{\text{3x}}{\text{1}-{\text{x}}^{\text{3}}}$ .

A. $P = \frac{\text{x}}{\text{x}-\text{1}}$

B. $P = \frac{1}{\text{x}-\text{1}}$

C. $P = \frac{\text{2}}{\text{1 - x}}$

D. $P = \frac{-1}{x - 1}$

Kết quả của bài toán $\frac{\text{1}}{\text{x}}+\frac{\text{1}}{\text{x(x}+\text{1)}}+\mathrm{...}+\frac{\text{1}}{\text{(x}+\text{9)(x}+\text{10)}}$  là?

A. $\frac{\text{x}+\text{20}}{\text{x(x}+\text{10)}}$

B. $\frac{\text{x}+\text{9}}{\text{x}+\text{10}}$

C. $\frac{\text{1}}{\text{x}+\text{10}}$

D. $\frac{\text{1}}{\text{x(x}+\text{1)}\mathrm{...}\text{(x}+\text{10)}}$

Cho $\frac{\text{1}}{\text{1}-\text{x}}+\frac{\text{1}}{\text{1}+\text{x}}+\frac{\text{2}}{\text{1}+{\text{x}}^{\text{2}}}+\frac{\text{4}}{\text{1}+{\text{x}}^{\text{4}}}+\frac{\text{8}}{\text{1}+{\text{x}}^{\text{8}}}=\frac{\mathrm{...}}{\text{1}-{\text{x}}^{\text{16}}}$ . Số thích hợp điền vào chỗ trống là?

A. 16

B. 8

C. 4

D. 20

Tìm a + b biết $\frac{{\text{x}}^{\text{2}}+\text{5}}{{\text{x}}^{\text{3}}-\text{3x}-\text{2}}=\frac{\text{a}}{\text{x}-\text{2}}+\frac{\text{b}}{{\text{(x}+\text{1)}}^{\text{2}}}$ ?

A. -2.

B. 1.

C. -1.

D. 2.

Tìm a, b sao cho $\frac{\text{4x}-\text{7}}{{\text{x}}^{\text{2}}-\text{3x}+\text{2}}=\frac{\text{a}}{\text{x}-\text{1}}+\frac{\text{b}}{\text{x}-\text{2}}$ ?

A. a = 3, b = 1.

B. a = -3, b = 1.

C. a = 3, b = -1.

D. a = -3, b = -1.

Tìm a, b sao cho $\frac{\text{1}}{\text{(x}+\text{1)(x}-\text{1)}}=\frac{\text{a}}{\text{x}+\text{1}}+\frac{\text{b}}{\text{x}-\text{1}}$

A. $a = \frac{-1}{2}; b = \frac{-1}{2}$

B. $a = \frac{1}{2}; b = \frac{1}{2}$

C. $a = \frac{1}{2}; b = \frac{-1}{2}$

D. $a = \frac{-1}{2}; b = \frac{1}{2}$

Cho 2a - b = 7; $a \ne \frac{-7}{3}$ ; $b \ne \frac{7}{2}$ . Tính giá trị của biểu thức

A = $\frac{\text{5a}-\text{b}}{\text{3a}+\text{7}}+\frac{\text{3b}-\text{2a}}{\text{2b}-\text{7}}$ .

A. 3

B. 4

C. 1

D. 2

Cho 3y - x = 6. Tính giá trị của biểu thức P = $\frac{\text{x}}{\text{y}-\text{2}}+\frac{\text{2x}-\text{3y}}{\text{x}-\text{6}}$ .

A. 3

B. 4

C. 1

D. 2

Kết luận nào sau đây là đúng khi nói về giá trị của biểu thức

M = $\frac{\text{10}}{\text{(x}+\text{2)(3}-\text{x)}}-\frac{\text{12}}{\text{(3}-\text{x)(3}+\text{x)}}-\frac{\text{1}}{\text{(x}+\text{3)(x}+\text{2)}}$  với x = -0,25?

A. M = 16.

B. M > 1.

C. M < 0.

D. 0 < M < 1.

Kết luận nào sau đây là đúng khi nói về giá trị của các biểu thức

B = $\frac{\text{x}}{{\text{x}}^{\text{3}}+\text{1}}+\frac{\text{1}-\text{x}}{{\text{x}}^{\text{2}}-\text{x}+\text{1}}+\frac{\text{1}}{\text{x}+\text{1}}$  với x = -2?

A. B > 0.

B. B < -1.

C. B < 0.

D. B > 1.

Giá trị của biểu thức P = $\frac{{\text{6x}}^{\text{2}}+\text{8x}+\text{7}}{{\text{x}}^{\text{3}}-\text{1}}+\frac{\text{x}}{{\text{x}}^{\text{2}}+\text{x}+\text{1}}-\frac{\text{6}}{\text{x}-\text{1}}$  với x = $\frac{1}{2}$ là?

A. -2

B. 2

C. $\frac{1}{2}$

D. $-\frac{1}{2}$

Giá trị của biểu thức C = $\frac{\text{1}}{\text{x}-\text{18}}-\frac{\text{1}}{\text{x}+\text{2}}$  với x = 2018 là?

A. $\frac{\text{1}}{\text{2020}}$

B. $\frac{\text{1}}{\text{202000}}$

C. $\frac{\text{1}}{\text{20200}}$

D. $\frac{\text{1}}{\text{200200}}$

Cho D = $\frac{{\text{5x}}^{\text{2}}}{\text{5x}-\text{6}}+\frac{{\text{x}}^{\text{2}}-\text{1}}{\text{6}-\text{5x}}-\frac{\text{7}+\text{x}-{\text{x}}^{\text{2}}}{\text{5x}-\text{6}}$ . Sau khi thu gọn hoàn toàn thì D có tử thức là?

A. x

B. x + 1

C. $\frac{\text{x}}{\text{x}-\text{1}}$

D. $\frac{\text{x}}{\text{x+1}}$

Cho B = $\frac{\text{1}}{{\text{x}}^{\text{2}}-\text{x}+\text{1}}+\text{1}-\frac{{\text{x}}^{\text{2}}+\text{2}}{{\text{x}}^{\text{3}}+\text{1}}$ . Sau khi thu gọn hoàn toàn thì B có tử thức là:

A. x

B. x + 1

C. $\frac{\text{x}}{\text{x}-\text{1}}$

D. $\frac{\text{x}}{\text{x+1}}$

Thu gọn biểu thức M = $\frac{{\text{4x}}^{\text{2}}-\text{3x}+\text{5}}{{\text{x}}^{\text{3}}-\text{1}}-\frac{\text{1}-\text{2x}}{{\text{x}}^{\text{2}}+\text{x}+\text{1}}-\frac{\text{6}}{\text{x}-\text{1}}$  ta được?

A. $\frac{-\text{12x}}{{\text{x}}^{\text{3}}-\text{1}}$

B. $\frac{-\text{12}}{{\text{x}}^{\text{3}}-\text{1}}$

C. $\frac{-\text{x}}{{\text{x}}^{\text{3}}-\text{1}}$

D. $\frac{3}{{\text{x}}^{\text{3}}-\text{1}}$

Thu gọn biểu thức A = $\frac{\text{3x}+\text{21}}{{\text{x}}^{\text{2}}-\text{9}}+\frac{\text{2}}{\text{x}+\text{3}}-\frac{\text{3}}{\text{x}-\text{3}}$  ta được?

A. $\frac{-\text{2}}{\text{x}-\text{3}}$

B. $\frac{\text{2x}}{\text{(x}-\text{3)(x}+\text{3)}}$

C. $\frac{\text{2}}{\text{x}+\text{3}}$

D. $\frac{\text{2}}{\text{x}-\text{3}}$

Thực hiện phép tính $\frac{\text{a}}{\text{a}+\text{1}}-\frac{\text{a}}{\text{a}-\text{1}}-\frac{{\text{2a}}^{\text{2}}}{\text{1}-{\text{a}}^{\text{2}}}$  ta được kết quả gọn nhất là?

A. $\frac{\text{2a}}{\text{a}-\text{1}}$

B. $\frac{{\text{2a}}^{\text{2}}+\text{2a}}{\text{(a}-\text{1)(a}+\text{1)}}$

C. $\frac{\text{2a}}{\text{a}+\text{1}}$

D. $-\frac{{\text{2a}}^{\text{2}}}{\text{(a}-\text{1)(a}+\text{1)}}$

Chọn câu sai?

A. $\frac{\text{11x}+\text{13}}{\text{3x}-\text{3}}+\frac{\text{15x}+\text{17}}{\text{4}-\text{4x}}=\frac{-\text{1}}{\text{12}}$

B. $\frac{\text{11x}+\text{13}}{\text{3x}-\text{3}}+\frac{\text{15x}+\text{17}}{\text{4}-\text{4x}}=\frac{-\text{x}-\text{1}}{\text{12(x}-\text{1)}}$

C. $\frac{\text{xy}}{{\text{x}}^{\text{2}}-{\text{y}}^{\text{2}}}-\frac{{\text{x}}^{\text{2}}}{{\text{y}}^{\text{2}}-{\text{x}}^{\text{2}}}=\frac{\text{x}}{\text{x}-\text{y}}$

D. $\frac{\text{xy}}{{\text{x}}^{\text{2}}-{\text{y}}^{\text{2}}}-\frac{{\text{x}}^{\text{2}}}{{\text{y}}^{\text{2}}-{\text{x}}^{\text{2}}}=\frac{-\text{x}}{\text{y}-\text{x}}$

Chọn câu đúng?

A. $\frac{\text{3x}-\text{4}}{{\text{4x}}^{\text{2}}{\text{y}}^{\text{5}}}+\frac{\text{9x}+\text{4}}{{\text{4x}}^{\text{2}}{\text{y}}^{\text{5}}}=\frac{\text{3}}{{\text{xy}}^{\text{4}}}$

B. $\frac{\text{2x}+\text{5}}{\text{3}}+\frac{\text{x}-\text{2}}{\text{3}}=\frac{\text{x}+\text{1}}{\text{3}}$

C. $\frac{\text{x}+\text{8}}{\text{x}-\text{1}}-\frac{\text{2x}-\text{1}}{\text{x}-\text{1}}-\frac{\text{6x}+\text{2}}{\text{x}-\text{1}}=\text{7}$

D. $\frac{\text{x}}{\text{x}-\text{y}}+\frac{\text{y}}{\text{x}+\text{y}}+\frac{{\text{2y}}^{\text{2}}}{{\text{x}}^{\text{2}}-{\text{y}}^{\text{2}}}=\frac{\text{x}+\text{y}}{\text{x}-\text{y}}$

Chọn câu đúng?

A. $\frac{\text{1}}{\text{x}+\text{2}}-\frac{\text{1}}{\text{(x}+\text{2)(4x}+\text{7)}}=\frac{\text{4x}}{\text{(x}+\text{2)(4x}+\text{7)}}$

B. $\frac{\text{2}-\text{21x}}{\text{18}}-\frac{\text{4}+\text{x}}{\text{12}}=\frac{\text{75x}-\text{16}}{\text{36}}$

C. $\frac{\text{1}}{\text{x}+\text{4}}-\frac{\text{1}}{\text{x}+\text{5}}=\frac{\text{1}}{\text{(x}+\text{4)(x}+\text{5)}}$

D. $\frac{\text{2}}{\text{x}-\text{5}}+\frac{\text{3x}}{{\text{x}}^{\text{2}}-\text{25}}=\frac{\text{4x}+\text{5}}{{\text{x}}^{\text{2}}-\text{25}}$

Điền vào chỗ trống: $\frac{\text{2x}-\text{6}}{\text{x}+\text{3}}-\mathrm{....}=\frac{\text{x}+\text{1}}{\text{2}}$ .

A. $\frac{-{\text{x}}^{\text{2}}+\text{15}}{\text{2(x}+\text{3)}}$

B. $\frac{{\text{x}}^{\text{2}}-\text{15}}{\text{2(x}+\text{3)}}$

C. $\frac{-{\text{x}}^{\text{2}}-\text{15}}{\text{2(x}+\text{3)}}$

D. Cả A, B, C đều sai

Kết quả gọn nhất của phép tính $\frac{\text{x}-\text{2}}{{\text{6x}}^{\text{2}}-\text{6x}}-\frac{\text{1}}{{\text{4x}}^{\text{2}}-\text{4}}$  là một phân thức có tử thức là?

A. $2x^2 + 5x - 4$

B. $\frac{{\text{2x}}^{\text{2}}-\text{5x}-\text{4}}{\text{12x(x}-\text{1)(x}+\text{1)}}$

C. $2x^2 - 4x - 4$

D. $2x^2 - 5x - 4$

Phép tính $\frac{\text{1}}{\text{x}+\text{1}}+\frac{\text{1}}{\text{1}-\text{x}}+\frac{{\text{2x}}^{\text{2}}}{{\text{x}}^{\text{2}}-\text{1}}$  có kết quả là?

A. $\frac{{\text{x}}^{\text{2}}+\text{2x}}{\text{(x}-\text{1)(x}+\text{1)}}$

B. 2

C. $\frac{{\text{2x}}^{\text{2}}+\text{2}}{\text{(x}-\text{1)(x}+\text{1)}}$

D. $\frac{{\text{2x}}^{\text{2}}}{{\text{x}}^{\text{2}}-\text{1}}$

Phép tính $\frac{\text{2}}{\text{x}+\text{3}}-\frac{\text{3}}{{\text{x}}^{\text{2}}-\text{9}}$  có kết quả là?

A. $\frac{\text{2x}-\text{9}}{{\text{x}}^{\text{2}}-\text{9}}$

B. $\frac{\text{2x}-\text{3}}{{\text{x}}^{\text{2}}-\text{9}}$

C. $\frac{\text{2x}-\text{9}}{\text{x}-\text{3}}$

D. $\frac{\text{x}-\text{6}}{{\text{x}}^{\text{2}}-\text{9}}$

Kết quả của tổng $\frac{\text{x}}{\text{xy}-{\text{y}}^{\text{2}}}+\frac{\text{2x}-\text{y}}{\text{xy}-{\text{x}}^{\text{2}}}$  là?

A. $\frac{-\text{x}+\text{y}}{\text{xy}}$

B. $\frac{\text{x}-\text{y}}{\text{x}}$

C. $\frac{\text{x}-\text{y}}{\text{y}}$

D. $\frac{\text{x}-\text{y}}{\text{xy}}$

Kết quả của tổng $\frac{\text{a}-\text{2}}{\text{a}-\text{b}}+\frac{\text{b}-\text{2}}{\text{b}-\text{a}}$  là?

A. -1

B. 1

C. $\frac{\text{a}-\text{b}}{\text{b}-\text{a}}$

D. $\frac{\text{a}+\text{b}-\text{4}}{\text{a}-\text{b}}$

Biểu thức x - 2 là kết quả của phép tính nào dưới đây?

A. $\frac{{\text{x}}^{\text{2}}+\text{4}}{\text{x}-\text{2}}-\frac{\text{4x}}{\text{2}-\text{x}}$

B. $\frac{{\text{x}}^{\text{2}}+\text{4}}{\text{x}-\text{2}}+\frac{\text{4x}}{\text{2}-\text{x}}$

C. $\frac{\text{2x}}{\text{x}-\text{2}}+\frac{\text{4}}{{\text{x}}^{\text{2}}-\text{4}}$

D. $\frac{\text{x}}{\text{x}-\text{2}}+\frac{\text{2}}{\text{x-2}}$

Phân thức $\frac{x - 1}{x + 1}$  là kết quả của phép tính nào dưới đây?

A. $\frac{\text{x}}{\text{x}+\text{1}}-\frac{\text{2}}{\text{x}+\text{1}}$

B. $\frac{\text{2x}}{\text{x}+\text{1}}-\frac{\text{2}}{\text{x}+\text{1}}$

C. $\frac{\text{x}}{\text{x}-\text{1}}+\frac{\text{1}}{\text{x}-\text{1}}$

D. $\frac{\text{x}}{\text{x}+\text{1}}+\frac{\text{1}}{\text{-x}-\text{1}}$

Thực hiện phép tính sau: $\frac{{\text{x}}^{\text{3}}}{{\text{x}}^{\text{2}}+\text{1}}+\frac{\text{x}}{{\text{x}}^{\text{2}}+\text{1}}$

A. -x

B. 2x

C. $\frac{x}{2}$

D. x

Kết quả thu gọn nhất của tổng $\frac{\text{2}-\text{3x}}{{\text{6x}}^{\text{2}}\text{y}}+\frac{\text{2x}+\text{1}}{{\text{6x}}^{\text{2}}\text{y}}+\frac{\text{2x}-\text{3}}{{\text{6x}}^{\text{2}}\text{y}}$  là?

A. $\frac{-\text{1}}{\text{6xy}}$

B. $\frac{\text{1}}{{\text{6x}}^{\text{2}}\text{y}}$

C. $\frac{\text{1}}{\text{6xy}}$

D. $\frac{\text{x}}{\text{6xy}}$

Phân thức đối của phân thức $\frac{-\text{x}}{\text{x}-\text{1}}$  là?

A. $\frac{\text{x}}{\text{x}-\text{1}}$

B. $\frac{\text{x}-\text{1}}{-\text{x}}$$\frac{-\text{x}}{-\text{x}-\text{1}}$

C. $\frac{-\text{x}}{-\text{x}-\text{1}}$

D. $\frac{\text{x}}{-\text{x}+\text{1}}$

Phân thức đối của phân thức $\frac{\text{3}}{\text{x}+\text{1}}$  là?

A. $\frac{-\text{3}}{\text{x}+\text{1}}$

B. $\frac{\text{x}+\text{1}}{\text{3}}$

C. $\frac{-\text{3}}{-\text{x}-\text{1}}$

D. $\frac{-\text{3}}{\text{x}-\text{1}}$

Chọn khẳng định đúng?

A. $\frac{\text{A}}{\text{B}}-\frac{\text{C}}{\text{D}}=\frac{\text{A}-\text{C}}{\text{B}-\text{D}}$

B. $\frac{\text{A}}{\text{B}}-\frac{\text{C}}{\text{D}}=\frac{\text{AD}}{\text{BC}}$

C. $\frac{\text{A}}{\text{B}}-\frac{\text{C}}{\text{D}}=\frac{\text{A}}{\text{B}}+\frac{-\text{C}}{\text{D}}$

D. $\frac{\text{A}}{\text{B}}-\frac{\text{C}}{\text{D}}=\frac{\text{A}-\text{C}}{\text{BD}}$

Với B ≠ 0, kết quả phép cộng $\frac{\text{A}}{\text{B}}+\frac{\text{C}}{\text{B}}$  là?

A. $\frac{\text{A.C}}{\text{B}}$

B. $\frac{\text{A+C}}{\text{B}}$

C. $\frac{\text{A+C}}{{\text{B}}^2}$

D. $\frac{\text{A+C}}{\text{2B}}$

Cho các phân thức $\frac{\text{1}}{\text{(a}-\text{b)(b}-\text{c)}}\text{;}\frac{\text{1}}{\text{(c}-\text{b)(c}-\text{a)}}\text{;}\frac{\text{1}}{\text{(b}-\text{a)(a}-\text{c)}}$ .

Bạn Mai nói rằng mẫu thức chung của các phân thức trên là (a - b)(b - c)(a - c).

Bạn Nhung nói rằng mẫu thức chung của các phân thức trên là (b - a)(c - b)(c - a).

Chọn câu đúng?

A. Bạn Mai đúng, bạn Nhung sai.

B. Bạn Mai sai, bạn Nhung đúng.

C. Hai bạn đều sai.

D. Hai bạn đều đúng.

Cho các phân thức $\frac{\text{11x}}{\text{3x}-\text{3}}\text{;}\frac{\text{5}}{\text{4}-\text{4x}}\text{;}\frac{\text{2x}}{{\text{x}}^{\text{2}}-\text{1}}$ .

Bạn Nam nói rằng mẫu thức chung của các phân thức trên là $6(x - 1){(x + 1)}^2$.

Bạn Minh nói rằng mẫu thức chung của các phân thức trên là 4(x - 1)(x + 1)

Chọn câu đúng?

A. Bạn Nam đúng, bạn Minh sai.

B. Bạn Nam sai, bạn Minh đúng.

C. Hai bạn đều sai

D. Hai bạn đều đúng.

Để có các phân thức có cùng mẫu, ta cần điền vào các chỗ trống $\frac{\text{x}+\text{3}}{{\text{x}}^{\text{2}}+\text{8x}+\text{15}}=\frac{\text{x}-\text{3}}{\mathrm{...}}\text{;}\frac{\text{5x}-\text{15}}{{\text{x}}^{\text{2}}-\text{6x}+\text{9}}=\frac{\mathrm{...}}{\text{(x}-\text{3)(x}+\text{5)}}$ các đa thức lần lượt là?

A. x - 3; 5x + 10

B. ${(x - 3)}^2(x + 5); 5x - 25$

C. (x - 3)(x + 5); 5x + 25

D. (x - 3)(x + 5); x + 5