Simplify :
(a-1 × b-1) ÷ (a-1 + b-1)
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Given,
Simplifying the expression :
⇒(a−1×b−1)÷(a−1+b−1)⇒(1a×1b)÷(1a+1b)⇒1ab÷b+aab⇒1ab×aba+b⇒1a+b.\Rightarrow (a^{-1} \times b^{-1}) ÷ (a^{-1} + b^{-1}) \\[1em] \Rightarrow \Big(\dfrac{1}{a} \times \dfrac{1}{b}\Big) ÷ \Big(\dfrac{1}{a} + \dfrac{1}{b}\Big) \\[1em] \Rightarrow \dfrac{1}{ab} ÷ \dfrac{b + a}{ab} \\[1em] \Rightarrow \dfrac{1}{ab} \times \dfrac{ab}{a + b} \\[1em] \Rightarrow \dfrac{1}{a + b}.⇒(a−1×b−1)÷(a−1+b−1)⇒(a1×b1)÷(a1+b1)⇒ab1÷abb+a⇒ab1×a+bab⇒a+b1.
Hence, a−1×b−1÷a−1+b−1=1a+ba^{-1} \times b^{-1} ÷ a^{-1} + b^{-1} = \dfrac{1}{a + b}a−1×b−1÷a−1+b−1=a+b1.
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(a-1 + b-1) ÷ (a-2 - b-2)
(a-1 + b-1) ÷ (ab)-1
(a + b)-1 × (a-1 + b-1)
(a+b+c)(a−1b−1+b−1c−1+c−1a−1)\dfrac{(a + b +c)}{(a^{-1}b^{-1} + b^{-1}c^{-1} + c^{-1}a^{-1})}(a−1b−1+b−1c−1+c−1a−1)(a+b+c)
