Simplify the rational expression $\frac{8x-42}{x^2+3x-18}$.

1. Problem Description

Simplify the rational expression $\frac{8x-42}{x^2+3x-18}$.

2. Solution Steps

First, we factor the numerator and the denominator.

The numerator is $8x - 42$. We can factor out a $2$ to get $2(4x - 21)$.

The denominator is $x^2 + 3x - 18$. We look for two numbers that multiply to $-18$ and add to $3$. These numbers are $6$ and $-3$. Therefore, the denominator factors as $(x+6)(x-3)$.

Now we rewrite the expression with the factored numerator and denominator:

$\frac{2(4x-21)}{(x+6)(x-3)}$

We cannot simplify this expression further because there are no common factors between the numerator and the denominator.

3. Final Answer

$\frac{2(4x-21)}{(x+6)(x-3)}$