We are asked to explain how to add and subtract rational expressions. Recall that a rational expression is a fraction whose numerator and denominator are polynomials.

Rational Expression : \frac{polynomial}{polynomial}

When adding and subtracting rational expressions we can use the same rules as when adding and subtracting numerical fractions. Therefore, we can add and subtract rational expressions only if they have the same denominator. If the expressions have different denominators, we can rewrite them using their least common denominator. Let's review these two cases!

Adding and Subtracting Rational Expressions With Like Denominators

If rational expressions have the same denominator, we add them by adding their numerators.

Sum	Add Numerators	Simplify Numerator
$\frac{1}{x ^{2}} + \frac{3}{x ^{2}}$	$\frac{1 + 3}{x ^{2}}$	$\frac{4}{x ^{2}}$
$\frac{y + 1}{2 y + 5} + \frac{2 y - 1}{2 y + 5}$	$\frac{y + 1 + 2 y - 1}{2 y + 5}$	$\frac{3 y}{2 y + 5}$
$\frac{z ^{2} + 3}{z + 1} + \frac{z - 1}{z + 1}$	$\frac{z ^{2} + 3 + z - 1}{z + 1}$	$\frac{z ^{2} + z + 2}{z + 1}$

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