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UKMT Intermediate Mathematical Challenge, 2021 Difficulty 3.0 AMC 10/12 Find the answer United Kingdom
What is the result when we simplify the expression ( 1 + 1 x ) ( 1 − 2 x + 1 ) ( 1 + 2 x − 1 ) \left(1 + \frac{1}{x}\right)\left(1 - \frac{2}{x+1}\right)\left(1 + \frac{2}{x-1}\right) ( 1 + x 1 ) ( 1 − x + 1 2 ) ( 1 + x − 1 2 )
(A) 1 1 1 1 x ( x + 1 ) \frac{1}{x(x+1)} x ( x + 1 ) 1 1 ( x + 1 ) ( x − 1 ) \frac{1}{(x+1)(x-1)} ( x + 1 ) ( x − 1 ) 1 1 x ( x + 1 ) ( x − 1 ) \frac{1}{x(x+1)(x-1)} x ( x + 1 ) ( x − 1 ) 1 x + 1 x \frac{x+1}{x} x x + 1
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