Simplify :
(a + b)-1.(a-1 + b-1)
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Simplifying the expression :
⇒(a+b)−1(a−1+b−1)=1(a+b)×(1a+1b)=1(a+b)×(b+aab)=1ab.\Rightarrow (a + b)^{-1}(a^{-1} + b^{-1}) = \dfrac{1}{(a + b)} \times \Big(\dfrac{1}{a} + \dfrac{1}{b}\Big) \\[1em] = \dfrac{1}{(a + b)} \times \Big(\dfrac{b + a}{ab}\Big) \\[1em] = \dfrac{1}{ab}.⇒(a+b)−1(a−1+b−1)=(a+b)1×(a1+b1)=(a+b)1×(abb+a)=ab1.
Hence, (a+b)−1(a−1+b−1)=1ab(a + b)^{-1}(a^{-1} + b^{-1}) = \dfrac{1}{ab}(a+b)−1(a−1+b−1)=ab1.
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