Prove that: (a+b)^-^1.(a^-^1 +b^-^1) = (ab)^-^1

Gijo Varghese asked May 16, 2023

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38 votes

Prove that:
(a+b)^-^1.(a^-^1 +b^-^1) = (ab)^-^1

Gijo Varghese asked May 16, 2023

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22 votes

Answer:

See below

Explanation:

(1)/(a+b) (
(1)/(a) +
(1)/(b) )

(1)/(a+b) (
(b)/(ab) +
(a)/(ab) )

(1)/(a+b) (
(b+a)/(ab) )

((a+b))/((a+b)(ab))

(1)/(ab)

ab^(-1)

Christylez answered May 23, 2023

3.3k points

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