Question

add the rational expressions and write the answer in simplest form. $\frac{2x}{x + 3}+\frac{x + 1}{x - 7}$
$\frac{5x - 3}{x - 4}$
$\frac{4x - 10}{2x - 4}$
$\frac{3x^{2}-10x + 3}{(x - 7)(x + 3)}$
$\frac{3x + 1}{-4}$

Explanation:

Step1: Find common denominator

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

Step2: Rewrite fractions with common denominator

$\frac{2x}{x + 3}\times\frac{x - 7}{x - 7}=\frac{2x(x - 7)}{(x + 3)(x - 7)}=\frac{2x^{2}-14x}{(x + 3)(x - 7)}$ and $\frac{x + 1}{x - 7}\times\frac{x + 3}{x + 3}=\frac{(x + 1)(x + 3)}{(x + 3)(x - 7)}=\frac{x^{2}+4x + 3}{(x + 3)(x - 7)}$.

Step3: Add the fractions

$\frac{2x^{2}-14x}{(x + 3)(x - 7)}+\frac{x^{2}+4x + 3}{(x + 3)(x - 7)}=\frac{2x^{2}-14x+x^{2}+4x + 3}{(x + 3)(x - 7)}=\frac{3x^{2}-10x + 3}{(x + 3)(x - 7)}$.

Answer:

$\frac{3x^{2}-10x + 3}{(x - 7)(x + 3)}$