Question

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

Answer 1

Step-by-step explanation:

follow the steps as shown in the picture and it will be proved. you know that raise to power -1 means u have to take resiprocal of the base no.

hope it will help

Answer 2

Hence proved  $(a^{-1}+b^{-1})^{-1}=\frac{ab}{a+b}$.

Step-by-step explanation:

To prove : $(a^{-1}+b^{-1})^{-1}=\frac{ab}{a+b}$

Proof :

Taking LHS,

$LHS=(a^{-1}+b^{-1})^{-1}$

$LHS=(\frac{1}{a}+\frac{1}{b})^{-1}$

$LHS=(\frac{b+a}{ab})^{-1}$

$LHS=\frac{ab}{a+b}$

$LHS=RHS$

Hence proved.

#Learn more

If 2(a^2+b^2)=(a+b)^2 prove that a=b

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