# Simplify rational expression

An algebraic expression where both the numerator and the denominator are polynomials e.g.

$$\frac{x+3}{x}$$

is called a rational expression. Since the denominator can't be zero there are values of x which are excluded from the rational expression. The expression above has an excluded value of zero.

To simplify a rational expression you have to eliminate all factors that are common of the numerator and the denominator. To accomplish this use the greatest common factor (GCF) of the factors e.g.

$$\frac{4xy}{6y^{2}} = \frac{2y\cdot 2x}{2y\cdot 3y} = \frac{ \color{red}{\cancel{2y} } }{ \color{red}{ \cancel{2y}}}\cdot \frac{2x}{3y}=\frac{2x}{3y}$$

**Video lesson**

Simplify rational expression

$$\frac{2p+6}{p^{2}+p-6}$$