Question

prove that
2/1+x^m-n+2/1+x^n-m=2​

Answer 1

$LHS = \frac{2}{1+x^{m-n}} + \frac{2}{1+x^{n-m}}$

$= \frac{2}{1+\frac{x^{m}}{x^{n}} }+ \frac{2}{1+\frac{x^{n}}{x^{m}}}$

$\boxed { \pink { Since ,x^{m-n} = \frac{x^{m}}{x^{n}} }}$

$= \frac{2}{\frac{x^{n} + x^{m}}{x^{n}}} + \frac{2}{\frac{x^{m} + x^{n}}{x^{m}}}$

$= \frac{2x^{n}}{x^{m} + x^{n} } + \frac{2x^{m}}{x^{m} + x^{n} }\\= \frac{2( x^{m}+ x^{n})}{x^{m}+x^{n}}\\= 2 \\= RHS$

$Hence\: proved$

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