# Thread: rational expressions. help plz!

1. ## rational expressions. help plz!

When mutiplying this...

x² - 5x + 4 X x² + 2x - 3
x² + 3x - 28 x² + 10x +21

...is to factor out?

But, what do i do if i can't find out factors?? Because im not sure how to factor them

2. Left Side:

$\displaystyle \frac {x^2 - 5x + 4}{x^2 + 3x - 28}$

Use the sum and product method.

The top equates to:

$\displaystyle (x-4)(x-1)$

And the bottom equates to:

$\displaystyle (x+7)(x-4)$

The $\displaystyle (x-4)$ terms cancel out so the left side of your expression is:

$\displaystyle \frac {x-1}{x+7}$

Right Side:

$\displaystyle \frac {x^2 + 2x - 3}{x^2 + 10x +21}$

The top equates to:

$\displaystyle (x+3)(x-1)$

The bottom equates to:

$\displaystyle (x+3)(x+7)$

The $\displaystyle (x+3)$ terms cancel out, so your right side expression is:

$\displaystyle \frac {x-1}{x+7}$

Rules of fractions say that we simply multiply the top by the top, and the bottom by the bottom to get:

$\displaystyle \frac {(x-1)^2}{(x+7)^2}$