Question

prove that ( a^-1 + b^-1)^-1= ab/a+b
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Answer 1

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

Take LHS

[ a^(-1) + b^(-1) ]^(-1)

Use, laws of exponents a^( - n) = 1/a^n

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

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

Use, laws of exponents ( a/b)^( - n) = ( b/a)^n

= ab / ( a + b)

= LHS

Hence proved.