Simple Algebraic Fractions/Rationa l Expressions Sessions 1 - 2

Objectives  Define rational expressions  Simplify rational expressions

RECALL: Simplifying numerical fractions

Simplify these fractions: 1. 2.

Division Property of Exponents  To divide powers that have the same base, you subtract the exponents.  For any base b ≠ 0 and positive integers m and n

Quotient of Powers Example 1: Write out as a product of factors. Cancel out common factors

Quotient of Powers Notice what we could have done using the property. Subtract exponents!

Quotient of Powers Example 2: Write out as a product of factors. Cancel out common factors!

Quotient of Powers Notice what we could have done using the property. Subtract exponents!

Quotient of Powers Example 3: Simplify top 1 st.

Power of a Quotient Property Example 4:

Example: 5

Algebraic Fraction/Rational Expression - A fraction whose numerator and denominator are polynomials Examples:

An algebraic fraction/rational expression is in lowest terms or simplest form if the numerator and denominator have no common factors other than 1 and -1.

Simplifying Algebraic Fractions/Rational Expressions 1) Factor the numerator and denominator completely. 2) Cancel common factors.

Simplify:

TRY THIS Exercise 4a, p. 119 numbers 6 – 10 (Notebooks)

Simplify the expression

REMEMBER: Cancellation is done after both numerator and denominator have been completely factorized.

SEATWORK Answer Exercise 4b – 1-10 (Notebooks)

Exercise 4b 1)

Exercise 4b 2)

Exercise 4b 3)

Exercise 4b 4)

Exercise 4b 5)

Exercise 4b 6)

Exercise 4b 7)

Exercise 4b 8)

Exercise 4b 9)

Exercise 4b 10)

Exercise 4b 11)

Exercise 4b 12)

Exercise 4b 13)

Exercise 4b 14)

Exercise 4b 15)

Exercise 4b 16)

Exercise 4b 17)

Exercise 4b 18)

Exercise 4b 19)

Exercise 4b 20)

Exercise 4b 21)

Exercise 4b 22)

PRACTICE TEST # 1 1)

PRACTICE TEST 2)

PRACTICE TEST 3)

PRACTICE TEST 4)

PRACTICE TEST 5)

PRACTICE TEST 6)

PRACTICE TEST 7)

PRACTICE TEST 8)