Adding and Subtracting Rational Expressions

Adding and Subtracting Rational Expressions

Open Ended

Describe how you found least common denominators (LCD)

How to Add/Subtract Rational Expressions

• Rewrite the denominators as factors to see what they have in common.

• Find the LCD (Least Common Denominator)

• Get both fractions to have a common denominator, then COMBINE the numerators and keep the denominator the same.

• Don't forget to distribute the negative in subtraction signs

Subtracting Rational Expressions!

• Same as adding rational expressions, but one extra thing!

• DISTRIBUTE THE NEGATIVE ALL THE WAY THROUGH

Multiple Choice

Simplify the expression

• $$\frac{6x}{20xy}$$

• $$\frac{3}{10y}$$

• $$\frac{6x+1}{20xy}$$

• $$\frac{3}{20xy}$$

Multiple Choice

Simplify the expression

• $$\frac{n}{2m}$$

• $$\frac{n}{3m}$$

• $$\frac{n}{4m}$$

• $$\frac{m^2+4n^2}{12m}$$

Multiple Choice

Multiple Choice

Subtract

Multiple Choice

Multiple Choice

Try on your own: Add the following expressions. Simplify Completely

• $$\frac{x-3}{5\left(x-8\right)}$$  

• $$\frac{3x-3}{x^2-2x-20}$$  

• $$\frac{x^2+2x-15}{5\left(x+5\right)\left(x-8\right)}$$  

• Can't add these

Multiple Choice

Try on your own: Subtract the following expressions. Simplify completely.

• $$\frac{x^2+4x-12}{\left(x-2\right)\left(x+2\right)\left(x+10\right)}$$

• $$\frac{x+6}{\left(x+2\right)\left(x+10\right)}$$

• $$\frac{x-6}{8x-24}$$

• Can't subtract these

Multiple Choice

Which expression is equivalent to $$\frac{y}{6}-\frac{3x}{4}+\frac{3}{2}$$

• $$\frac{20y-9x}{12}$$

• $$\frac{11y-9x}{12}$$

• $$\frac{13y-6x}{8}$$

• $$\frac{10y-6x}{6}$$

Multiple Choice

What is the LCD of the rational expression $$\frac{9x}{x-2},\ \frac{x}{2},\frac{9}{x^2-4}$$

• $$x^2-4$$

• $$2\left(x-2\right)$$

• $$2\left(x-2\right)^2$$

• $$2\left(x^2-4\right)$$

Open Ended

A women drives an SUV that gets 10 mi/gal (mpg). Her husband drives a hybrid that gets 60 mpg. Every week, they travel the same number of miles. They want to improve their combined mpg. They have two options on how they can improve it.

Option 1: They can tune the SUV and increase its mileage by 1 mpg a

Multiple Select

What do you have to do when adding or subtracting rational expressions? Check all that apply.

• Find a common denominator

• Solve for x

• Simplify completely

• Nothing

• Distribute the negative (Subtracting only)

Poll

How confident are you with adding/subtracting rational expressions?