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