Prove that

(a^-1 + b^-1)^-1 = ab/a+b

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Solution

We know that
(a^-1+b^-1)^-1
=1/(1/a+1/b)
Now make the denominator equal of 1/a+1/b
So then it will become
1/(a/ab+b/ab)
That is 1/(a+b/ab)
Now the "ab" will come to the numerator side
that is ab/a+b
Hence poved

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