Question

prove it with complete explanation with each and every step ​

Answer 1

Answer:

Here is your solution.

Answer 2

${\huge{\bold{\purple{\bigstar{\boxed{\boxed{\bf{Question}}}}}}}}$

Prove that

$\sf\dfrac{a+b+c}{a^{-1}b^{-1} + b^{-1}c^{-1} + c^{-1}a^{-1}} = abc$

${\huge{\bold{\purple{\bigstar{\boxed{\boxed{\bf{Solution}}}}}}}}$

$\implies\sf\dfrac{a+b+c}{a^{-1}b^{-1} + b^{-1}c^{-1} + c^{-1}a^{-1}} = abc$

$\implies\sf\dfrac{a+b+c}{\dfrac{1}{ab} + \dfrac{1}{bc}+\dfrac{1}{ca}} = abc$

$\implies\sf\dfrac{a+b+c}{\dfrac{a+b+c}{abc}} = abc$

$\implies\sf\dfrac{\cancel{a+b+c}}{\cancel{a+b+c}} \times abc= abc$

$\sf\implies abc = abc$

${\bold{\blue{\boxed{\bf{abc= abc }}}}}$

${\bold{\blue{\boxed{\bf{LHS= RHS }}}}}$

${\bold{\blue{\boxed{\bf{\dag Hence\: proved}}}}}$

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