Semester Exam Review

What is a rational expression?

​Simplifying Rational Expressions

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

​Reduce to lowest terms.

Example

​Step 1: Factor the numerator and denominator

Step 2: Cancel/cross out common terms

​Step 1: factor the numerator 3(x - 3)

factor the denominator (x - 3) (x + 3)

Step 2 Cancel Cross out common terms

3 / (x + 3)

Multiple Choice

• A

• B

• C

• D

Multiple Choice

Simplify the rational expression.

Multiple Choice

Simplify $$\frac{\left(a-2\right)\left(a+2\right)}{\left(a+2\right)\left(a-3\right)}$$  

• $$\frac{a-2}{a-3}$$  

• $$\frac{a+2}{a-3}$$  

• $$\frac{a-2}{a+3}$$  

• $$\frac{a}{a+2}$$  

Operations with Polynomials

• We can add them.

• We can subtract them.

• We can multiply them.

• We can divide them.

• And any other mathematical iteration...

Multiplying Rational Expressions

• Step 1 See if any of the expressions can be simplified.

• Step 2 Multiply the numerators.

• Step 3 Multiply the denominators.

• Step 4 Simplify if you can.

Let's apply this to rational expressions!

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.

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

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

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

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

• $$\frac{2x^2-x-3}{x-4}$$  

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!

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

Multiply the following expressions.

$$\frac{x^2-8x+12}{x^2-16}\cdot\frac{4x+16}{x^2-4x+4}$$  

• $$\frac{4\left(x-6\right)}{\left(x-4\right)\left(x-2\right)}$$  

• $$\frac{\left(x-4\right)\left(x-2\right)}{4\left(x-6\right)}$$  

• $$\frac{x-6}{x-2}$$  

• $$\frac{4}{x-4}$$  

Poll

How confident do you feel about your ability to multiply/divide rational expressions?

• Very Confident

• Pretty good, but need more practice

• Definitely need more practice

• Help me!