Question

prove that: (a+b)-1(a-1+b-1)=(ab)-1​

Answer 1

Correct Question

$\sf(a^{-1}+b^{-1})^{-1}=\dfrac{ab}{a+b}$

Solution

☀️ Need To Prove : 

$\sf{(a^{-1}+b^{-1})^{-1}=\dfrac{ab}{a+b}}$

☀️ Proof :

$\sf{Taking \ LHS,}$

⇢ $\sf{LHS=(a^{-1}+b^{-1})^{-1}}$

⇢ $\sf{LHS=(\dfrac{1}{a}+\dfrac{1}{b})^{-1}}$

⇢ $\sf{LHS=(\dfrac{b+a}{ab})^{-1}}$

⇢ $\sf{LHS=\dfrac{ab}{a+b}}$

$\sf{LHS = RHS}$

Hence proved.