Adding and Subtracting Rational Expressions with Like Denominators

To add (or subtract) two or more rational expressions with the same denominators, add (or subtract) the numerators and place the result over the denominator.

If $a$ , $b$ , and $c$ represent polynomials (with $c\ne 0$ ), then

$\frac{a}{c}+\frac{b}{c}=\frac{a+b}{c}$

and

$\frac{a}{c}-\frac{b}{c}=\frac{a-b}{c}$ .

Example 1:

Add $\frac{n}{n+3}+\frac{2}{n+3}$ .

Since the denominators are the same, just add the numerators.

$\frac{n}{n+3}+\frac{2}{n+3}=\frac{n+2}{n+3}$

Example 2:

Subtract $\frac{1}{2-b}-\frac{4}{2-b}$ .

Since the denominators are the same, just subtract the numerators.

$\begin{array}{l}\frac{1}{2-b}-\frac{4}{2-b}=\frac{1-4}{2-b}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=\frac{-3}{2-b}\end{array}$