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# Algebra/How do I subtract this equation with variables?

Question

The problem.
Hello,

I am currently reviewing for my upcoming math class placement test. I got to this one algebra problem that has just stumped me. You can see the equation in the attached image. Due to formatting restrictions I can not actually include it in my question.

Anyway, I know that I have to factor the denominators to get a common denominator. So far I have not been able to crack this puzzle. In particular, the single x that is not squared or cubed, in the first fraction, has been really confusing me. I just don't know what to do with it.

Any tips on how to solve this kind of problem would be greatly appreciated.

Thanks,
Elizabeth

To do this, first the bases need to factored.
It's just like math where prime factors are found.
Instead of prime factors, we need to factor what's there.

The 1st fraction is 1/[(x+3)(x-2)].
The 2nd fraction is 1/[(x+3)(x-3)].

It can be seen from here that the 1st fraction needs to be multiplied by (x-3)/(x-3)
and the 2nd fraction needs to multiplied by (x-2)(x-2).

This gives us 2(x-3)/[(x+3)(x-3)(x-2)] - (x-2)/[(x+3)(x-3)(x-2)].

They can now be combined, giving (2x - 6 - x + 2)/[(x+3)(x-3)(x-2)].
Simplifying the top gives (x - 4)/[(x+3)(x-3)(x-2)].

If the bottom is rearranged slightly, the answer is there.

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#### Scott A Wilson

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