Question

subtract the rational expressions and write the answer in simplest form. $\frac{x + 1}{x - 7}-\frac{2x}{x + 3}$
$\frac{x + 1}{x - 4}$
$\frac{3x + 1}{2x - 4}$
$\frac{-x^{2}+18x + 3}{(x - 7)(x + 3)}$
$\frac{-x - 1}{-4}$

Explanation:

Step1: Find common denominator

The common denominator of $\frac{x + 1}{x - 7}$ and $\frac{2x}{x + 3}$ is $(x - 7)(x + 3)$.

Step2: Rewrite fractions with common denominator

$\frac{(x + 1)(x + 3)}{(x - 7)(x + 3)}-\frac{2x(x - 7)}{(x - 7)(x + 3)}=\frac{(x + 1)(x + 3)-2x(x - 7)}{(x - 7)(x + 3)}$

Step3: Expand numerators

Expand $(x + 1)(x + 3)=x^{2}+3x+x + 3=x^{2}+4x + 3$ and $2x(x - 7)=2x^{2}-14x$. Then the numerator becomes $x^{2}+4x + 3-(2x^{2}-14x)=x^{2}+4x + 3 - 2x^{2}+14x=-x^{2}+18x + 3$.

Answer:

$\frac{-x^{2}+18x + 3}{(x - 7)(x + 3)}$