Dividing Rational Expressions

Dividing Rational Expressions

​Similar to multiplying rational expressions with one extra step in the beginning

Can't divide by fractions so we have to flip it. (Keep Change Flip)

Then we follow the steps to multiply rational expressions!

Dividing Rational Expressions

• Just like multiplying rational expressions with one extra step

• Always flip the rational expression that you are dividing by (second fraction or fraction in the denominator)

Dividing Rational Expressions

​Step 1: Change the division to multiply by the reciprocal. (Flip the fraction)

Step 2: Simplify by factoring.

Step 3: Cross out common factors.

​Steps/Strategy:

1. Same Change Flip

2. Factor Everything

3. Simplify

   1. Reduce Monomials

   2. Cancel Common Binomial Factors

4. The final answer is whatever is left in the numerator and denominator written as a single fraction

Dividing rational expressions.

EXAMPLE NO. 1

Step 1: Copy, Change and Flip

Step 2: Factor the numerator and denominator

Step 3: Cancel Common factors

Step 4: Multiply the remaining factors

EXAMPLE NO. 2

Step 1: Copy, Change and Flip

Step 2: Factor the numerator and denominator

Step 3: Cancel Common factors

Step 4: Multiply the remaining factors

Multiple Choice

Divide the following expressions.

• $$\frac{y^{\ 4}}{2x^2}$$

• $$\frac{9y^8}{2x^4}$$

• $$\frac{2x^2}{y^{\ 4}}$$

• Can't be simplified

Multiple Choice

Divide the following expressions.

• $$\frac{4\left(x-4\right)}{\left(x+5\right)}$$

• $$\frac{\left(x+4\right)^2\left(x-4\right)}{16\left(x+5\right)}$$

• Can't be simplified

• $$\frac{\left(x+5\right)}{4\left(x-4\right)\ }$$

Multiple Choice

Simplify completely.

$$\frac{n-5}{n^2-4n-5}\div\frac{1}{6n}$$  

• $$\frac{8}{n+2}$$  

• $$\frac{n-4}{8}$$  

• $$\left(n+10\right)\left(n-7\right)$$  

• $$\frac{6n}{n+1}$$  

Multiple Choice

Simplify completely.

$$\frac{1}{a-4}\div\frac{a-6}{5a^2-20a}$$  

• $$\frac{2a\left(a+7\right)}{a+3}$$  

• $$\frac{5a}{a-6}$$  

• $$a-7$$  

• $$\frac{a+7}{a+3}$$  

Multiple Choice

Simplify completely.

$$\frac{8x+24}{8}\div\frac{x+3}{3}$$  

• $$\frac{\left(x+6\right)\left(x-5\right)}{9x}$$  

• $$3$$  

• $$\frac{3}{2}$$  

• $$\frac{3}{x+8}$$  

Multiple Choice

Divide the rational expression and state the excluded values.

• $$\frac{1}{6},\ x\ne-10,\ -8,\ 8$$

• $$\frac{x+10}{6x+60},\ x\ne-8,\ 8$$

• $$\frac{x+8}{6x+60},\ x\ne-8,\ 8$$

• $$\frac{x+8}{x-8},\ x\ne-10,\ -8$$

Multiple Choice

Divide the following expressions.

• $$\frac{4\left(x-4\right)}{\left(x+5\right)}$$

• $$\frac{\left(x+4\right)^2\left(x-4\right)}{16\left(x+5\right)}$$

• Can't be simplified

• $$\frac{\left(x+5\right)}{4\left(x-4\right)\ }$$