Multiplying rational expressions

Rational Expressions

​Factor the numerator and denominator first Cancel/cross out common terms

Multiplying Rational Expressions

• Factor the numerator and denominator (if possible)

• Cancel/cross our common terms or expressions

• Multiply straight across (numerator by numerator, denominator by denominator)

Multiple Choice

Multiply and divide, simplify, and give the domain.

$$\frac{8x^5y}{25z^3}\cdot\frac{15z^3}{20xy^4}$$  

• $$\frac{6x^4}{25y^3}$$  

• $$\frac{18x^4}{15y^3z}$$  

• $$\frac{18x^3yz}{25}$$  

• $$\frac{6x^3z^2}{15y}$$  

Multiple Choice

Multiply and divide, simplify, and give the domain (two answer choices).

$$\frac{27a^3b^5}{8ab}\cdot\frac{12a^2}{b^3}$$  

• $$\frac{81a^4b}{2}$$  

• $$\frac{39a^4}{7b}$$  

• $$\frac{39a^2b^3}{8}$$  

• $$\frac{54a^2}{7b}$$  

Multiple Choice

Multiply and simplify

$$\frac{x^2+x-30}{x-7}\cdot\frac{2x-14}{x+6}$$  

• $$2\left(x+5\right)$$  

• $$2\left(x-5\right)$$  

• $$\frac{\left(2x-14\right)\left(x-5\right)}{x-7}$$  

• $$\frac{x+6}{x-5}$$  

Multiple Choice

Multiply and simplify.

$$\frac{x^2-x-6}{x^2-2x-8}\cdot\frac{2x^2-x-3}{x^2-3x-4}$$  

• $$\frac{\left(x-3\right)\left(2x-3\right)}{\left(x-4\right)^2}$$  

• $$\frac{\left(x-3\right)\left(2x-3\right)}{x^2-4^{ }}$$  

• $$\frac{\left(x+3\right)\left(x+1\right)}{\left(x-4\right)\left(x+2\right)}$$  

• $$\frac{2x^2-x-3}{x-4}$$  

Multiple Choice

Multiply and simplify.

$$\frac{4x+8}{x^2-25}\cdot\frac{x-5}{5x+10}$$  

• $$\frac{4}{5\left(x-5\right)}$$  

• $$\frac{4}{5\left(x+5\right)}$$  

• $$\frac{4\left(x-5\right)}{5\left(x^2-25\right)}$$  

• $$\frac{5x-3}{x^2+5x-15}$$  

Multiple Choice

Multiply the following expressions.

• $$\frac{2x^4+4x^2-72x^2-144x}{4x^3+8x^2-144x-288}$$

• $$1$$

• $$\frac{x}{2}$$

• Can't be simplified