Ok, so I'm doing a comprehensive math review of algebra, Cal I, and Cal II before starting Cal III in the fall semester. I got a B in Cal II so I'm doing "ok" (should have had an A, but these pesky algebra snags...) but I have run into a bit of a problem that I can't quite figure out.
The problem is:
2/a2 - 3/ab + 4/b2 (answer: 2b2 - 3ab + 4a2 / a2b2 )
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/a2 - 3/ab
Now I tried using ad - bc / bd for this, and it got me:
2(ab) - 3(a2 ) / a2(ab)
Simplify: 2ab - 3a2 / a3b
This isn't correct why? When I use a web based algebra calculator it says this should net me 2b - 3a / a2b - 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...