Question

Prove that $\frac{1}{x+x^{p-q}}+\frac{1}{1+x^{q/-p}}=1$

Answer 1

To prove: $\frac{1}{1+x^{p-q}}+\frac{1}{1+x^{q-p}}=1$

L.H.S:-

$\frac{1}{1+\frac{x^p}{x^q}}+\frac{1}{1+\frac{x^q}{x^p}}$

$\Rightarrow \frac{x^q}{x^q+x^p}+\frac{x^p}{x^p+x^q}$

$\Rightarrow \frac{x^q+x^p}{x^p+x^q}=1\Rightarrow$ L.H.S=R.H.S

Hence Proved