Dear Student , 11+xa-b+11+xb-a=1Taking L H S=11+xa-b+11+xb-a=11+xaxb+11+xbxa=xbxb+xa+xaxa+xb=xa+xbxa+xb=1Hence L H S=R H S proved Regards

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Dear Student ,

\frac{1}{1 + x^{a - b}} + \frac{1}{1 + x^{b - a}} = 1 Taking L . H . S = \frac{1}{1 + x^{a - b}} + \frac{1}{1 + x^{b - a}} = \frac{1}{1 + \frac{x^{a}}{x^{b}}} + \frac{1}{1 + \frac{x^{b}}{x^{a}}} = \frac{x^{b}}{x^{b} + x^{a}} + \frac{x^{a}}{x^{a} + x^{b}} = \frac{x^{a} + x^{b}}{x^{a} + x^{b}} = 1 Hence L . H . S = R . H . S proved

Regards