# How do you simplify (x^2-7x+12) / (x-4) ?

Feb 17, 2016

You must factor the numerator to see if anything can eliminate itself.

#### Explanation:

$\frac{{x}^{2} - 7 x + 12}{x - 4}$

To factor a trinomial of the form $a {x}^{2} + b x + c , a = 1$, you must find two numbers that multiply to c and that add to b. Two numbers that do this are -4 and -3.

= $\frac{\left(x - 3\right) \left(x - 4\right)}{x - 4}$

Since dividing a number by itself gives one, the x - 4 in the numerator and the x - 4 in the denominator eliminate themselves. This leaves us with $x - 3$ as our answer.

The key for simplifying rational expressions: always factor completely to see what you can eliminate!!. Also, as you will see in the practice exercises, it is most helpful to factor out the GCF (greatest common factor) before engaging in other types of factorization.

Practice exercises:

1. Simplify the following rational expressions.

a) $\frac{4 x + 8}{x + 2}$

b) $\frac{3 {x}^{2} + 6 x}{{x}^{2} - 4}$

c) $\frac{{x}^{2} - 9 x - 22}{{x}^{2} - 15 x + 44}$

Good luck!