Simplifying Issue: a^-1 + 1 / b^-1 - 1 (ans. is (a+b)^2/ab?)

[DeadAngelicHeart]

Hello Everyone,

I have been having a very hard time trying to figure out exactly how I am supposed to siplify the following expression:

a^-1+1
_______
b^-1 -1

The answer I am givin in the end is (a+b)^2
ab

Can someone please help me and explain step by step how to simplify this equation.

Thank You!

 

[Loren]

Re: Simplifying Issue

Something seems to be wrong somewhere. If a=2 and b=3 the original expression is -9/4 and(a+b)[sup:jg12756b]2[/sup:jg12756b] = 25.

\(\displaystyle \frac{a^{-1}+1}{b^{-1}-1}=\frac{\frac{1}{a}+1}{\frac{1}{b}-1}\)

Now, multiply both numerator and denominator by ab and see what you get. I don't think it will be anything like what you say it's supposed to be.

 

[Denis]

Re: Simplifying Issue

The answer I am givin in the end is (a+b)^2
ab

WHO in heck gave you that as answer ; no wonder you're getting nowhere :shock: