Question

prove that : a+b+c/a^-1×b^-1+b^-1×c^-1+c^-1×a^-1=abc
please please please answer it

Answer 1

from R. H. S

$\frac{a + b + c}{a {}^{ - 1} \times b {}^{ - 1} + b {}^{ - 1} \times c {}^{ - 1} + c {}^{ - 1} \times a {}^{ - 1} } \\ \\ = \frac{a + b + c}{ \frac{1}{a} \times \frac{1}{b} + \frac{1}{b} \times \frac{1}{c} + \frac{1}{c} \times \frac{1}{a} } \\ \\ = \frac{a + b + c}{ \frac{1}{ab} + \frac{1}{bc} + \frac{1}{ca} } \\ \\ = \frac{a + b + c}{ \frac{c + a + b}{abc} } \\ \\ = \frac{(a + b + c)abc}{(a + b + c)} \\ \\ = abc$
= R. H. S.

proved

hope it helps....