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SSC CHSL 2023 PYQ — Question 52

SSC CHSL - 09 March 2023 - Shift 1 • Quantitative Aptitude • Q52

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What is the value of 1+x21−x÷1−x4x−1×x(1−x)(1+x)\frac{1+x^2}{1-x}\div \frac{1-x^4}{x-1}\times \frac{x(1-x)}{(1+x)}?

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Correct answer: C

Explanation

The correct answer is Option 3 i.e. −x(1+x)2\frac{-x}{(1+x)^2}.

1+x21−x÷1−x4x−1×x(1−x)(1+x)\frac{1+x^2}{1-x}\div \frac{1-x^4}{x-1}\times \frac{x(1-x)}{(1+x)}

=1+x21−x×x−11−x4×x(1−x)(1+x)= \frac{1+x^2}{1-x} \times \frac{x-1}{1-x^4} \times \frac{x(1-x)}{(1+x)}

=1+x21−x×−(1−x)(1−x2)(1+x2)×x(1−x)(1+x)= \frac{1+x^2}{1-x} \times \frac{-(1-x)}{(1-x^2)(1+x^2)} \times \frac{x(1-x)}{(1+x)}

=−1(1+x)×x(1+x)= \frac{-1}{(1+x)} \times \frac{x}{(1+x)}

=−x(1+x)2=\frac{-x}{(1+x)^2}