Question

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

Answer:

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Answer 2

Step-by-step explanation:

Given : ${(a + b)}^{ - 1} ( {a}^{ - 1} + {b}^{ - 1} ) = {(ab)}^{ - 1}$

L.H.S. : ${(a + b)}^{ - 1} ( {a}^{ - 1} + {b}^{ - 1} )$

{Identity : x ⁻¹ = 1/x }

→ $( \frac{1}{a + b} ) (\frac{1}{a} + \frac{1}{b} )$

→ $(\frac{1}{a + b} ) (\frac{a + b}{ab})$

→ $\dfrac{1}{ab}$

→ ${(ab)}^{ - 1}$

= R.H.S.

Hence, proved !!