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Prove that a^1/ a^-1+ b^-1 + a^-1/ a^-1- b^-1 |
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Answer» Answer: To PROVE that a-1 /a-1 +b-1 +a-1 /a-1 -b-1 = 2b2 /b2 -a2Lets take the LHS (LEFT Hand Side) first: =1/a÷1/a+1/b + 1/a÷1/a -1/b Next take the LCM for the denominator, so it BECOMES: =1/a÷b+a /ab + 1/a÷b-a /ab =1/a×ab /b+a+ 1/a×ab /b-a Now 'a' gets cancelled in both the numerator and the denominator. So it becomes: =1/a×ab /b+a+ 1/a×ab /b-a =b /b+a+b /b-a take the LCM of the denominator and so it becomes: =b(b-a)/(b+a)(b-a)+b(b+a)/(b-a)(b+a) =b2 -ab /b2 -A2 +b2 +ab /b2 -a2 =b2 -ab +b2 +ab /b2 -a2 =b2+b2/b2-a2 =2b2/b2 -a2 ==== RHS (Right Hand Side) Step-by-step explanation: |
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