Multiplying and Dividing Rational Expressions

Multiplying and Dividing Rational Expressions.

​Multiplying Rational Expressions.

*When Multiplying Rational Expressions - Remember to Factor the numerator and denominator of each expression. Cancel out like factors.

Multiple Choice

$$\frac{\left(x+9\right)\left(x+8\right)}{8}\cdot\frac{\left(x-1\right)}{\left(x+8\right)\left(x-1\right)}$$  

• $$\frac{\left(x+9\right)}{8}$$   

• $$\frac{\left(x-1\right)}{8}$$  

• $$\frac{1}{8}$$  

•   $$\frac{\left(x+9\right)\left(x+8\right)}{8}$$  

Multiple Choice

Multiply and Simplify

• 4(x+3)/(x+2),

• (x+2)/4(x+1)

• (x+2)/4(x+3),

• 4(x+1)/(x+2),

Multiple Choice

$$\frac{x^2-x-6}{x-3}\cdot\frac{x+9}{x+2}$$  

• $$x+9$$  

• $$\frac{x-3}{x-2}$$  

• $$\frac{x+9}{x+2}$$  

• $$x-3$$  

Multiple Choice

Multiply & Simplify: $$\frac{x^3-9x}{x^2+10x+21}\cdot\frac{x^2+7x}{x^2+5x-24}$$  

• $$\frac{2x}{x+8}$$  

• $$\frac{x^2}{x+8}$$  

• $$\frac{x}{x+4}$$  

• $$\frac{x^2\left(x-9\right)}{x+8}$$  

Dividing Rational Expressions

When Dividing Rational Expressions - Multipy by the inverse, then factor and simplify.

Multiple Choice

Divide the Rational Expression

• A

• B

• C

• D

Multiple Choice

Divide and Simplify

• 1/6

• x+10/ 6x+60

• x+8/ 6x+60 

• (x+10)(x+8)/ 6x+60

Multiple Choice

Divide the Rational Expression

• A

• B

• C

• D

Complex Expressions

A Complex Expression is a Rational Expression divided by another Rational Expression.

Re-Write it and Treat it as a Division Problem

Multiple Choice

Simplify: $$\frac{\frac{1}{k+3}}{\frac{7k^2}{k^2+7k+12}}$$  

• k + 3

• k - 10

• $$\frac{k-5}{3}$$  

• $$\frac{k+4}{7k^2}$$  

Multiple Choice

Simplify:  $$\frac{\frac{x}{5}}{\frac{4}{x+6}}$$  

• $$\frac{4x}{5\left(x+6\right)}$$  

• $$20x\left(x+6\right)$$  

• $$\frac{x\left(x+6\right)}{20}$$  

• $$\frac{x+6}{20x}$$  

Multiple Choice

Simplify: $$\frac{\frac{5k^3-25k^2}{5k^2}}{\frac{k^2+2k-35}{9}}$$  

• $$\frac{4k^2}{k-7}$$  

• $$\frac{9}{k+7}$$  

• $$\frac{9}{4}$$  

• 1