5.4 Multiply & Divide Rational Expressions How do you simplify fractions made up of rational functions?

Simplified form of a rational expression - Means the numerator and denominator have NO common factors. If the numerator and/or denominator are polynomials, factor them ALL THE WAY, then “cancel” common factors. (x+?) or (x-?) is a package deal—don’t break it up! ** Hint for simplifying: FACTOR EVERYTHING FIRST!!

Factor Completely. 9x2 + 30x + 25 4x2 -16x +16 3x2 -17x +10

Examples: Simplify.

More Examples: Simplify. (Hint: Factor everything first!!)

Another example even yet: Simplify.

Hey, how about ANOTHER Example!

You say you want MORE examples?

THE LAST EXAMPLE!!!

A company makes a tin to hold flavored popcorn A company makes a tin to hold flavored popcorn. The tin is a rectangular prism with a square base. The company is designing a new tin with the same base and twice the height of the old tin. Packaging See page 328 • Find the surface area and volume of each tin. • Calculate the ratio of surface area to volume for each tin. • What do the ratios tell you about the efficiencies of the two tins?

How do you simplify fractions made up of rational functions? Factor and reduce

5.4 Assignment p. 331 7-19 odd, 25-43 odd