Question

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Answer 1

TO PROVE :-

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

PROOF :-

LHS =

$\frac{a + b + c}{ {a}^{ - 1} {b}^{ - 1} + {b}^{ - 1} {c}^{ - 1} + {c}^{ - 1} {a}^{ - 1} } \\ \\ \\ = \frac{a + b + c}{ \frac{1}{a} \times \frac{1}{b} + \frac{1}{b} \times \frac{1}{c} + \frac{1}{c} \times \frac{1}{a}} \\ \\ \\ = \frac{a + b + c}{ \frac{1}{ab} + \frac{1}{bc} + \frac{1}{ca} } \\ \\ \\ = \frac{a + b + c}{ \frac{c + a + b}{abc} } \\ \\ \\ = (a + b + c ) \: \div \frac{a + b + c}{abc} \\ \\ \\ = (a + b + c) \: \times \frac{abc}{(a + b + c)} \\ \\ \\ = abc$

= RHS

Hence, we proved it.

LAWS USED :-

a^ -1 = 1/a

a/b ÷ c/d = a/b × d/c

Answer 2

Step-by-step explanation:

a+b+c/1/ab+1/bc+1/ca= abc

a+b+c/c+a+b/abc=abc

a+b+c X abc/a+b+c  = abc

abc= abc  

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