The problem is:

2/a

^{2}- 3/ab + 4/b

^{2}(answer: 2b

^{2}- 3ab + 4a

^{2}/ a

^{2}b

^{2})

With other fractions that have non-matching denominators I have been working the method ad + or - bc / bd has worked every time, no troubles...except now. This method fails on this problem and I want to understand why. This is the kind of thing that cost me points in Cal II and I don't want that happening in Cal III.

First thing I did was break the problem into chunks, the first chunk consisting of:

2/a

^{2}- 3/ab

Now I tried using ad - bc / bd for this, and it got me:

2(ab) - 3(a

^{2}) / a

^{2}(ab)

Simplify: 2ab - 3a

^{2}/ a

^{3}b

This isn't correct why? When I use a web based algebra calculator it says this should net me 2b - 3a / a

^{2}b - how is it that the method that works with every other complex fraction I have been doing doesn't work for this problem?

Of course, if I keep going with what I have and do ad + bc / bd I get something that ends up being WAY OFF. I know I could find the common denominator, but I always thought that the method ad + or - bc / bd was a more efficient way to do things...

This is driving me insane, please help me regain my sanity so I can make the appropriate notes and move on to another review section...