Factoring with fractions

HOME

Math Central

Quandaries & Queries

Question from Megan, a student:

Hi there,
I'm working on factoring polynomials but this question has me quite puzzled.. im a college student in my first year.

(x^2-a^2/xy)(xy/x+a)

I don't understand after you factor the separate brackets, how you multiply the numerator by the denominator, and then how you multiply the equation in the first bracket by the second..
If you could please help me that would be great!

Hi Megan,

First you factor the $x^2 - a^2$ to get $(x - a)(x + a)$ and then you have

\[\frac{(x - a)(x + a)}{xy} \times \frac{xy}{x + a}\]

At this point you can cancel the $xy$ in the denominator of the first fraction with the $xy$ in the numerator of the second fraction. Likewise you can cancel the $(x + a)$ factor that occurs in both fractions.

Penny

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.