## Doing a comprehensive review, need fraction help...

Quadratic equations and inequalities, variation equations, function notation, systems of equations, etc.
I_Feel_Dumb
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### Doing a comprehensive review, need fraction help...

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...

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Joined: Sun Feb 22, 2009 11:12 pm

### Re: Doing a comprehensive review, need fraction help...

The problem is:

2/a2 - 3/ab + 4/b2
This is just an expression. Until they give you instructions, there is no problem do resolve.
(answer: 2b2 - 3ab + 4a2 / a2b2 )
My guess is that they forgot to tell you to "convert to a common denominator and combine".
With other fractions that have non-matching denominators I have been working the method ad + or - bc / bd has worked every time
What is this "method"? Why not just do common denominators like for numerical fractions? They show how here: http://www.purplemath.com/modules/rtnladd.htm

You have this:

. . .$\dfrac{2}{a^2}\, -\, \dfrac{3}{ab}\, +\, \dfrac{4}{b^2}$

The factors in the denominators are aa, ab, and bb. You can find the LCM (aabb) using the charting method they show here: http://www.purplemath.com/modules/lcm_gcf.htm

Then multiply each fraction by what it needs so it ends up with aabb in the denominators:

. . .$\left(\dfrac{2}{a^2}\right)\, \left(\dfrac{b^2}{b^2}\right)$

. . .$\left(\dfrac{3}{ab}\right)\, \left(\dfrac{ab}{ab}\right)$

. . .$\left(\dfrac{4}{b^2}\right)\, \left(\dfrac{a^2}{a^2}\right)$