Simplifying, Multiplying, and Dividing Rational Expressions

Rational expressions are fractions that contain polynomials, like $\frac{2x+4}{x-3}$. Just like with number fractions, we can simplify them by canceling common factors.

When simplifying rational expressions, first factor both the numerator and denominator. Then identify and cancel any common factors. Remember to note any excluded values – values that make the denominator zero!

Multiplying rational expressions works just like multiplying fractions: multiply the numerators together and multiply the denominators together. Then simplify your answer by factoring and canceling common terms.

Dividing rational expressions? Simply flip the second fraction (find its reciprocal) and multiply! For example, to calculate $\frac{a}{b} ÷ \frac{c}{d}$, rewrite it as $\frac{a}{b} × \frac{d}{c}$.

Pro Tip: Always factor completely before canceling terms. Don't try to cancel individual variables or numbers unless they're part of a common factor in both the numerator and denominator!

Complex fractions (fractions within fractions) might look intimidating, but they can be simplified by treating them as division problems. Just remember your order of operations, and you'll master rational expressions in no time!