Question

question #6
perform the indicated operation for the given rational expressions:
$\frac{x + 6}{3x^{2}-12x}-\frac{3x - 3}{3x^{2}-12x}$. write the answer in simplest form.
$\frac{-2x - 9}{3x^{2}-12x}$
$\frac{4x + 3}{3x^{2}-12x}$
$\frac{2x + 3}{3x^{2}-12x}$
$\frac{-2x + 9}{3x^{2}-12x}$

Explanation:

Step1: Combine numerators

Since the denominators are the same ($3x^{2}-12x$), we subtract the numerators: $(x + 6)-(3x - 3)$.
$(x + 6)-(3x - 3)=x + 6-3x + 3$.

Step2: Simplify the combined - numerator

Combine like - terms: $x-3x+6 + 3=-2x+9$.
The resulting rational expression is $\frac{-2x + 9}{3x^{2}-12x}$.

Answer:

$\frac{-2x + 9}{3x^{2}-12x}$