Bell Ringer 3-7-18 Simplify 3𝑥 6𝑥 Simplify 2𝑥−4 6𝑥+2 Factor (x2 – 9) Factor (x2 + 4x + 4) Factor (x3 – 8)

Simplifying Rational Expressions Wednesday, March 7, 2018

Rational Expressions are Fractions with variables.

Excluded Values With fractions, you can not have a denominator of zero because you cannot divide by zero. Remember The 1st Commandment of Math is “Thou Shalt Not Divide By Zero” Anything that makes a denominator of a Rational Expression zero is an Excluded Value.

Simplify Apply the properties of exponents and factoring polynomials.

Review: Properties of Exponents When we multiply, we add. When we divide, we subtract. When we raise a power to a power, we multiply. When we raise a product to a power, we distribute. When we raise a quotient to a power, we distribute. Anything to the zero power is 1. To make a negative exponent positive, flip its location.

Polynomial of 4 or more terms Binomial 1. GCF 2. Difference of Squares 3. Difference of Cubes 4. Sum of Cubes Review: Factoring Trinomial 1. GCF 2. Perfect Square Trinomial 3. “Unfoil” or “Unbox” Polynomial of 4 or more terms 1. GCF 2. Factor by Grouping

Examples 1. 18 𝑥 6 27 𝑥 4 2. 16 𝑎 2 𝑏 3 𝑐 4 20 𝑎 7 𝑏 2 𝑐 2 3. 𝑥 2 +9𝑥+20 2𝑥+8 4. 𝑥 2 −6𝑥+8 𝑥 2 +2𝑥−24

Practice! Classwork: Simplifying Rational Expressions ODD Homework: Simplifying Rational Expressions EVEN

Exit Ticket 1. Rational Expressions are _________, so we treat them the same way. 2. We simplify by using the ____ of _________ and by _________ to cancel out anything both in the numerator and denominator. 3. We look for extraneous solutions by seeing what will make the __________ 0.