# How do you simplify (3x)/(x²-3x-18)- ( x-4)/(x-6)?

##### 1 Answer
Feb 17, 2016

First, factor the first denominator (${x}^{2} - 3 x - 18$) to see what has to be our LCD (Least Common Denominator)

#### Explanation:

To factor a trinomial of form $a {x}^{2} + b x + c , a = 1$, you must find two numbers that multiply to c and that add to b. These numbers are -6 and +3.

$\frac{3 x}{\left(x - 6\right) \left(x + 3\right)}$

The LCD of the expression is (x - 6)(x + 3).

= $\frac{3 x}{\left(x - 6\right) \left(x + 3\right)} - \frac{\left(x - 4\right) \left(x + 3\right)}{\left(x - 6\right) \left(x + 3\right)}$

= $\frac{3 x - \left({x}^{2} - 4 x + 3 x - 12\right)}{\left(x - 6\right) \left(x + 3\right)}$

= $\frac{3 x - {x}^{2} + 4 x - 3 x + 12}{\left(x - 6\right) \left(x + 3\right)}$

= $\frac{- {x}^{2} + 4 x + 12}{\left(x - 6\right) \left(x + 3\right)}$

= $\frac{- {x}^{2} + 4 x + 12}{{x}^{2} - 3 x - 18}$