SOLUTION: Hi, I'm really stuck on this question: (1/a + 1/b) / {(1/a^2)-(1/b^2)} Where do I even start?? Please have clear step by step explanation. Thanks so much!!

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: Hi, I'm really stuck on this question: (1/a + 1/b) / {(1/a^2)-(1/b^2)} Where do I even start?? Please have clear step by step explanation. Thanks so much!!       Log On


   

Question 1017833: Hi, I'm really stuck on this question:
(1/a + 1/b) / {(1/a^2)-(1/b^2)}
Where do I even start?? Please have clear step by step explanation. Thanks so much!!
Answer by FrankM(1040) About Me  (Show Source):
You can put this solution on YOUR website!
Here's the important thing to understand:
%28A%2BB%29%28A-B%29=A%5E2-B%5E2%29
if we rearrange the equation we get
%28A%2BB%29%2F%28A%5E2-B%5E2%29=%28A-B%29%29
And we can see that your expression simplifies to
%281%2Fa+-+1%2Fb%29+
Because
%281%2Fa%5E2%29-%281%2Fb%5E2%29 factors to

%281%2Fa+-+1%2Fb%29+%281%2Fa+%2B+1%2Fb%29