Question

Please tell question number 4 part 1...

Answer 1

Answer :



$l.h.s \: = > \\ \\ \frac{1}{1 + {x}^{a - b} } + \frac{1}{1 + {x}^{b - a} } \\ \\ write \: all \: numerators \: above \: l.c.m \\ \\ \frac{1 + {x}^{b - a} + 1 + x {}^{a - b} }{(1 + {x}^{a - b} )(1 + {x}^{b - a}) } \\ \\ \frac{2 + {x}^{b - a} + {x}^{a - b} }{1 + {x}^{b - a} + {x}^{a - b} + 1} \\ \\ \frac{2 + {x}^{b - a} + {x}^{a - b} }{2 + {x}^{b - a} + {x}^{a - b} } \\ \\ any \: expression \: divided \: by \: itself \: equals \: to \: 1 \\ \\ = > \: 1 \\ \\ l.h.s = r.h.s \\ \\ hence \: proven.$



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