4/x+3 +3x/x-2+5x+2/4-x2

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· 14:37 22/02/2025

4/x+3 +3x/x-2+5x+2/4-x²

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xixin

1 năm trước

\[
\frac{4}{x+3} + \frac{3x}{x-2} + \frac{5x + 2}{-(x^2 - 4)}
\]

- For \( \frac{4}{x+3} \):
\[
\frac{4}{x + 3} \cdot \frac{(x - 2)(x + 2)}{(x - 2)(x + 2)} = \frac{4(x - 2)(x + 2)}{(x + 3)(x - 2)(x + 2)}
\]

- For \( \frac{3x}{x - 2} \):
\[
\frac{3x}{x - 2} \cdot \frac{(x + 3)(x + 2)}{(x + 3)(x + 2)} = \frac{3x(x + 3)(x + 2)}{(x - 2)(x + 3)(x + 2)}
\]

- For \( \frac{5x + 2}{-(x^2 - 4)} \):
\[
\frac{5x + 2}{-(x - 2)(x + 2)} \cdot \frac{(x + 3)}{(x + 3)} = \frac{-(5x + 2)(x + 3)}{(x - 2)(x + 2)(x + 3)}
\]

\[
\frac{4(x - 2)(x + 2) + 3x(x + 3)(x + 2) - (5x + 2)(x + 3)}{(x + 3)(x - 2)(x + 2)}
\]

- \( 4(x - 2)(x + 2) = 4(x^2 - 4) = 4x^2 - 16 \)
- \( 3x(x + 3)(x + 2) = 3x(x^2 + 5x + 6) = 3x^3 + 15x^2 + 18x \)
- \( -(5x + 2)(x + 3) = -(5x^2 + 15x + 2x + 6) = -5x^2 - 17x - 6 \)

\[
4x^2 - 16 + 3x^3 + 15x^2 + 18x - 5x^2 - 17x - 6
\]

\[
3x^3 + (4x^2 + 15x^2 - 5x^2) + (18x - 17x) + (-16 - 6) = 3x^3 + 14x^2 + x - 22
\]

= \[
\frac{3x^3 + 14x^2 + x - 22}{(x + 3)(x - 2)(x + 2)}
\]

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1 năm trước

4x+3+3xx−2+5x+2−(x2−4)4x+3+3xx−2+5x+2−(x2−4)

- For 4x+34x+3:
4x+3⋅(x−2)(x+2)(x−2)(x+2)=4(x−2)(x+2)(x+3)(x−2)(x+2)4x+3⋅(x−2)(x+2)(x−2)(x+2)=4(x−2)(x+2)(x+3)(x−2)(x+2)

- For 3xx−23xx−2:
3xx−2⋅(x+3)(x+2)(x+3)(x+2)=3x(x+3)(x+2)(x−2)(x+3)(x+2)3xx−2⋅(x+3)(x+2)(x+3)(x+2)=3x(x+3)(x+2)(x−2)(x+3)(x+2)

- For 5x+2−(x2−4)5x+2−(x2−4):
5x+2−(x−2)(x+2)⋅(x+3)(x+3)=−(5x+2)(x+3)(x−2)(x+2)(x+3)5x+2−(x−2)(x+2)⋅(x+3)(x+3)=−(5x+2)(x+3)(x−2)(x+2)(x+3)

4(x−2)(x+2)+3x(x+3)(x+2)−(5x+2)(x+3)(x+3)(x−2)(x+2)4(x−2)(x+2)+3x(x+3)(x+2)−(5x+2)(x+3)(x+3)(x−2)(x+2)

- 4(x−2)(x+2)=4(x2−4)=4x2−164(x−2)(x+2)=4(x2−4)=4x2−16
- 3x(x+3)(x+2)=3x(x2+5x+6)=3x3+15x2+18x3x(x+3)(x+2)=3x(x2+5x+6)=3x3+15x2+18x
- −(5x+2)(x+3)=−(5x2+15x+2x+6)=−5x2−17x−6−(5x+2)(x+3)=−(5x2+15x+2x+6)=−5x2−17x−6

4x2−16+3x3+15x2+18x−5x2−17x−64x2−16+3x3+15x2+18x−5x2−17x−6

3x3+(4x2+15x2−5x2)+(18x−17x)+(−16−6)=3x3+14x2+x−223x3+(4x2+15x2−5x2)+(18x−17x)+(−16−6)=3x3+14x2+x−22

= 3x3+14x2+x−22(x+3)(x−2)(x+2)

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