# Having trouble with high school algebraic fractions

• Jan 20th 2013, 11:12 AM
KevinShaughnessy
Having trouble with high school algebraic fractions
Hi,

I'm having a bit of trouble with the work I was assigned by my teacher. The problem goes:

1/(3-x) + (2x-5)/(x²-7x+12)

The common denominator is supposed to be (x-3)(x-4) and the answer is supposed to be x-1/cd. The problem is that two of the common denominator terms have the same variables but different signs, namely (3-x) and (x-3). I'm supposed to simplify out one of those factors and then switch the operator between the fractions so that this becomes a subtraction problem. The thing is I don't know which one of the factors to remove, which factor to multiply the numerator by, and how I should proceed in general. Can anyone help me?

Thanks!
• Jan 20th 2013, 11:27 AM
Plato
Re: Having trouble with high school algebraic fractions
Quote:

Originally Posted by KevinShaughnessy
1/(3-x) + (2x-5)/(x²-7x+12)
The common denominator is supposed to be (x-3)(x-4) and the answer is supposed to be x-1/cd.

Note that $\frac{1}{(3-x)}+\frac{2x-5}{x^2-7x+12}=\frac{2x-5}{(x-3)(x-4)}-\frac{1}{(x-3)}$.

Now can you see LCD?
• Jan 20th 2013, 12:45 PM
HallsofIvy
Re: Having trouble with high school algebraic fractions
You need to know that 3- x= -(x- 3).
• Jan 20th 2013, 01:01 PM
KevinShaughnessy
Re: Having trouble with high school algebraic fractions
Awesome, it makes sense now. Thanks guys, I really appreciate it!