# Multiply rational expressions

You multiply rational expressions in the same way as you multiply fractions of rational numbers. In other words you multiply the numerators with each other and the denominators with each other.

**Example**

$$\frac{4xy^{2}}{3y}\cdot \frac{2x}{4y}=$$

$$=\frac{4xy^{2}\cdot 2x}{3y\cdot 4y}=\frac{8x^{2}y^{2}}{12y^{2}}=\frac{{\color{red} {\not}}{4}\cdot 2x^{2}{\color{red} {\not}}{y^{2}}}{{\color{red}{ \not}}{4}\cdot 3{\color{red} {\not}}{y^{2}}}=\frac{2x^{2}}{3}$$

You can either start by multiplying the expressions and then simplify the expression as we did above or you could start by simplifying the expressions when it's still in fractions and then multiply the remaining terms e.g.

$$\frac{4xy^{2}}{3y}\cdot \frac{2x}{4y}=$$

$$=\frac{{\color{red} {\not}}{4}xy^{2}\cdot 2x}{3y\cdot{\color{red} {\not}}{4}y}=\frac{2x^{2}{\color{red} {\not}}{y^{2}}}{3{\color{red} {\not}}{y^{2}}}=\frac{2x^{2}}{3} $$

**Video lesson**

Multiply the rational expressions

$$\frac{4xy^{2}}{3y}\cdot \frac{5x^{2}}{2y}$$