x/(x-1)+1/(x+1)+2 x/(1-x²)= ? · ABC26GN1000

Subject: General Aptitude · Chapter: Simplification

$\frac{x}{x-1}+\frac{1}{x+1}+\frac{2 x}{1-x^{2}}=$ ?

(a)1

(b)2

(c)3

(d)4

Answer

Answer (as printed): A

Explanation

$$\begin{aligned} \frac{x}{x-1}+\frac{1}{x+1}+\frac{2 x}{1-x^{2}} & =\frac{x}{x-1}+\frac{1}{x+1}-\frac{2 x}{x^{2}-1} \\ & =\frac{x(x+1)+(x-1)-2 x}{\left(x^{2}-1\right)} \\ & =\frac{x^{2}+x+x-1-2 x}{x^{2}-1}=\frac{x^{2}-1}{x^{2}-1}=1 . \end{aligned}$$

Explanation as extracted from the printed page; notation may be imperfect.

Study loop for Simplification

1. Practise the PYQsPrevious-year questions, with answers

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