Prove that: (i) 11+xa−b+11+xb−a=1 (ii) 11+xb−a+xc−a+11+xa−b+

1.	Prove that: (i) 11+xa−b+11+xb−a=1 (ii) 11+xb−a+xc−a+11+xa−b+xc−b+11+xb−c+xa−c=1
Answer» Prove that: (i) $\frac{1}{1 + x^{a - b}} + \frac{1}{1 + x^{b - a}} = 1$ (ii) $\frac{1}{1 + x^{b - a} + x^{c - a}} + \frac{1}{1 + x^{a - b} + x^{c - b}} + \frac{1}{1 + x^{b - c} + x^{a - c}} = 1$

Prove that: (i) 11+xa−b+11+xb−a=1 (ii) 11+xb−a+xc−a+11+xa−b+xc−b+11+xb−c+xa−c=1

Answer»

Prove that:

(i) $\frac{1}{1 + x^{a - b}} + \frac{1}{1 + x^{b - a}} = 1$

(ii) $\frac{1}{1 + x^{b - a} + x^{c - a}} + \frac{1}{1 + x^{a - b} + x^{c - b}} + \frac{1}{1 + x^{b - c} + x^{a - c}} = 1$