SOLUTION: Please help me understand . The equation is : ( a^-1 + b^-1)^2 . I need to simplify it. The answer is (b^2+2ab+a^2)/a^2*b^2. Can you explain why. Why after using a common deno

Algebra ->  Algebra  -> Expressions-with-variables -> SOLUTION: Please help me understand . The equation is : ( a^-1 + b^-1)^2 . I need to simplify it. The answer is (b^2+2ab+a^2)/a^2*b^2. Can you explain why. Why after using a common deno      Log On

Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

   

Question 121022: Please help me understand .
The equation is : ( a^-1 + b^-1)^2 . I need to simplify it. The answer is (b^2+2ab+a^2)/a^2*b^2.
Can you explain why. Why after using a common denominator , the " 2ab" is out of the fraction?
Thank you . Viktor
Answer by nabla(475) About Me  (Show Source):
You can put this solution on YOUR website!
I presume you are able to get to this step: 1%2Fa%5E2+%2B+1%2Fb%5E2+%2B+2%2F%28a%2Ab%29
Now, what is the common denominator? a%5E2%2Ab%5E2
Multiply each term by what it is missing to form the common denominator:
1%2Fa%5E2%2A%28b%5E2%2Fb%5E2%29+%2B+1%2Fb%5E2%2A%28a%5E2%2Fa%5E2%29+%2B+2%2F%28a%2Ab%29%2A%28a%2Ab%2F%28a%2Ab%29%29.
As you can see, the numerator becomes b%5E2%2Ba%5E2%2B2a%2Ab, and the denominator is a%5E2%2Ab%5E2.