SSC CHSL 2022 PYQ — Question 58

The correct answer is option 3 i.e.  $\frac{2mn}{x^n(n^2-m^2)}$

Calculations:

⇒ mx^m - nxⁿ = 0

⇒ mx^m = nxⁿ

⇒ m/n = x^m/xⁿ

We can take, m = x^m and n = xⁿ

Now according to the question,

⇒ $\frac{1}{m+n}+\frac{1}{m-n}$

⇒ $\frac{n - m + n + m}{(n + m)(n - m)}$

⇒ 2n/(n² - m²)

$\frac{1}{x^m+x^n}+\frac{1}{x^m-x^n}$ in terms of xⁿ

⇒ $\frac{2n}{n^2- m^2} \times \frac{x^n}{x^n}$

⇒ $\frac{2n x^n}{(n^2- m^2)x^n}$

⇒ $\frac{2nm}{(n^2- m^2)x^n}$