1/20/ :24 AM10.3 Multiplying and Dividing Expressions1 Simplify, Multiply and Divide Rational Expressions Section 8-2

Simplify Example 1

Simplify Example 2 1 2

1/20/ :24 AM10.3 Multiplying and Dividing Expressions4 Example 3 Simplify Step 1: Is there a GCF? Step 2: Factor the numerator (s) of x 2 + 6x + 9 Step 3: Factor the denominator(s) x Step 4: Cancel out the factors if needed and then multiply. No (x + 3) (x + 3) (x - 3)

1/20/ :24 AM10.3 Multiplying and Dividing Expressions5 Example 4 Simplify

1/20/ :24 AM10.3 Multiplying and Dividing Expressions6 Rules of Multiplying Expressions 1.Take GCF of numerator(s) and denominator(s) if possible. 2.Factor the numerator(s) and denominator (s) 3.Cancel [up and down OR diagonally] out the factors if needed, multiply and simplify.

1/20/ :24 AM10.3 Multiplying and Dividing Expressions7 Example 5 Simplify 2 2

1/20/ :24 AM10.3 Multiplying and Dividing Expressions8 Example 6 Simplify

1/20/ :24 AM10.3 Multiplying and Dividing Expressions9 Undefined Values Any number substituted into a variable which makes the expression in the denominator equal to zero, it will cause the equation to be undefined. Quick Steps: –After factoring an expression, put all factors equal to zero –Solve for the variable –Answers are the restrictions

1/20/ :24 AM10.3 Multiplying and Dividing Expressions10 Example 7 Simplify. Identify any x-values for which the expression is undefined. (3x + 4) (3x + 4)(x – 1)

1/20/ :24 AM10.3 Multiplying and Dividing Expressions11 Example 8 Simplify Identify any x-values for which the expression is undefined. (2x + 1) (2x – 3)

1/20/ :24 AM10.3 Multiplying and Dividing Expressions12 Example 9 Simplify. Identify any x-values for which the expression is undefined. Factor out –1 in the numerator so that x 2 is positive, and reorder the terms. Factor the numerator and denominator. Divide out common factors. –1(x 2 – 4x) x 2 – 2x – 8 –1(x)(x – 4) (x – 4)(x + 2) –x–x (x + 2 ) Simplify.

1/20/ :24 AM10.3 Multiplying and Dividing Expressions13 Rules of Divide Expressions 1.Take GCF of numerator(s) and denominator(s) if possible. 2.Take the reciprocal (flip) of the second fraction. 3.Factor the numerator(s) and denominators into simplest form 4.Cancel out the factors and cancel if needed, 5.Multiply and simplify

1/20/ :24 AM10.3 Multiplying and Dividing Expressions14 Example

1/20/ :24 AM10.3 Multiplying and Dividing Expressions15 Example 11 Simplify

1/20/ :24 AM10.3 Multiplying and Dividing Expressions16 Example 12 Simplify

1/20/ :24 AM10.3 Multiplying and Dividing Expressions17 Your Turn Simplify and/or solve these problems x 2 – 9 2x + 3 = 5 6x – x 2 x 2 – 7x + 6

1/20/ :24 AM10.3 Multiplying and Dividing Expressions18 Example 13 Simplify

1/20/ :24 AM10.3 Multiplying and Dividing Expressions19 Example 14 Solve. Check your solution and list restrictions of Note that x ≠ 5. (x + 5)(x – 5) (x – 5) = 14 x + 5 = 14 x = 9

1/20/ :24 AM10.3 Multiplying and Dividing Expressions20 Example 15 Solve. Check your solution and list restrictions of

1/20/ :24 AM10.3 Multiplying and Dividing Expressions21 Assignment Pg 580: