Algebraic fraction

An algebraic fraction is a fraction where the top and the bottom are algebraic expressions. Two examples of algebraic fractions are $\frac{3x}{x^2+2x-3}$ and $\frac{\sqrt{x+2}}{x^2-3}$.

A rational fraction is an algebraic fraction where the top and the bottom are polynomials. $\frac{3x}{x^2+2x-3}$ is a rational fraction, but $\frac{\sqrt{x+2}}{x^2-3}$ is not. This is because the top has a square root function.

Operations

Multiplication

$\frac{x^2+9x+20}{x^2-4}\cdot \frac{x+2}{x+4}$

$=\frac{(x+4)(x+5)}{(x+2)(x-2)}\cdot \frac{x+2}{x+4}$

$=\frac{x+5}{x-2}$

Division

Turn the equation into multiplication by flipping one of the fractions. After that, do what is shown above.

$\frac{x^2+9x+20}{x^2-4}÷\frac{x+2}{x+4}=\frac{x^2+9x+20}{x^2-4}\cdot \frac{x+4}{x+2}$