If mxᵐ- nxⁿ = 0, then the value of 1 over xᵐ+xⁿ + 1 over xᵐ-xⁿ in terms of xⁿis : Where x, m, n are > 0.

If mxᵐ- nxⁿ = 0, then the value of 1 over xᵐ+xⁿ + 1 over…

If mx^m- nxⁿ = 0, then the value of ${{1} \over x^m+x^n}$ + ${{1} \over x^m-x^n}$ in terms of xⁿis :

Where x, m, n are > 0.

Show answer & explanation

Correct answer: D

Explanation

The correct answer is option 4 i.e. $\frac{2mn}{x^n(n^2-m^2)}$

mx^m- nxⁿ = 0

x^m = nxⁿ/m

then the value of ${{1} \over x^m+x^n}$ + ${{1} \over x^m-x^n}$

= $\frac{x^m+x^n+x^m-x^n}{(x^m+x^n)(x^m-x^n)}$

Put the value of x^m

= (2nxⁿ/m)/[(nxⁿ/m + xⁿ)(nxⁿ/m - xⁿ)]

= (2nxⁿ/m)/[xⁿ $(\frac{n+m}{m})(\frac{n-m}{m})$ ]

= 2mn/[xⁿ(n² - m²)]