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1 câu trả lời 206
Let's simplify the expression step by step:
The given expression is: (x−1x+1−x+1x−1+x2−1x2−4x−1)⋅xx+3
First, let's simplify the terms inside the parentheses. Notice that x2−1=(x−1)(x+1). We can rewrite the first two fractions with a common denominator of (x−1)(x+1):
(x−1)(x+1)(x+1)(x+1)−(x+1)(x−1)(x−1)(x−1)+(x−1)(x+1)x2−4x−1
(x−1)(x+1)(x+1)2−(x−1)(x+1)(x−1)2+(x−1)(x+1)x2−4x−1
Now, expand the numerators: (x+1)2=x2+2x+1 (x−1)2=x2−2x+1
Substitute these back into the expression: (x−1)(x+1)(x2+2x+1)−(x2−2x+1)+(x2−4x−1)
Simplify the numerator: (x2+2x+1−x2+2x−1+x2−4x−1) (x2+(2x+2x−4x)+(1−1−1)) x2+0x−1 x2−1
So, the expression inside the parentheses becomes: (x−1)(x+1)x2−1
Since x2−1=(x−1)(x+1), we have: (x−1)(x+1)(x−1)(x+1)=1
Now, multiply this result by the second fraction: 1⋅xx+3=xx+3
Final Answer: The final answer is xx+3
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