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Multiplying and Dividing Expressions
Section 11.1 © 2012,
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8.4: Multiply and Divide Rational Expressions
Quick Review Factor x2 + 6x + 9 Factor x2 – 9 11/24/2018 5:02 AM 8.4: Multiply and Divide Rational Expressions
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Rules of Simplifying Expressions
Take GCF of numerator(s) and denominator(s) if possible. Factor the numerator(s) (top) into simplest form Factor the denominator(s) (bottom) into the simplest form Cancel [bottom or cross] out the factors if needed, multiply and simplify. Apply the GCF to the factors, then… FACTOR, CANCEL, QUIT. 11/24/2018 5:02 AM 8.4: Multiply and Divide Rational Expressions
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8.4: Multiply and Divide Rational Expressions
Example 1 Simplify Don’t do this way!! NO! 11/24/2018 5:02 AM 8.4: Multiply and Divide Rational Expressions
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8.4: Multiply and Divide Rational Expressions
Example 1 Simplify Step 1: Is there a GCF? Step 2: Factor the numerator (s) Step 3: Factor the denominator(s) Step 4: Cancel out the factors if needed and then multiply. No (x + 3) (x + 3) (x + 3) (x – 3) 11/24/2018 5:02 AM 8.4: Multiply and Divide Rational Expressions
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8.4: Multiply and Divide Rational Expressions
Example 2 Simplify 11/24/2018 5:02 AM 8.4: Multiply and Divide Rational Expressions
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8.4: Multiply and Divide Rational Expressions
Your Turn Simplify 11/24/2018 5:02 AM 8.4: Multiply and Divide Rational Expressions
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8.4: Multiply and Divide Rational Expressions
Example 3 Simplify 11/24/2018 5:02 AM 8.4: Multiply and Divide Rational Expressions
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8.4: Multiply and Divide Rational Expressions
Your Turn Simplify 11/24/2018 5:02 AM 8.4: Multiply and Divide Rational Expressions
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Rules of Multiplying Expressions
Take GCF of numerator(s) and denominator(s) if possible. Factor the numerator(s) (top) into simplest form Factor the denominator(s) (bottom) into the simplest form Cancel [bottom or cross] out the factors if needed, multiply and simplify. Apply the GCF to the factors, then… FACTOR, CANCEL, QUIT. 11/24/2018 5:02 AM 8.4: Multiply and Divide Rational Expressions
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8.4: Multiply and Divide Rational Expressions
Rational Functions Add Subtract Common Denominator Multiply Divide Cancel 11/24/2018 5:02 AM 8.4: Multiply and Divide Rational Expressions
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8.4: Multiply and Divide Rational Expressions
Example 4 Simplify 11/24/2018 5:02 AM 8.4: Multiply and Divide Rational Expressions
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8.4: Multiply and Divide Rational Expressions
Example 5 Simplify 11/24/2018 5:02 AM 8.4: Multiply and Divide Rational Expressions
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8.4: Multiply and Divide Rational Expressions
Your Turn Simplify 11/24/2018 5:02 AM 8.4: Multiply and Divide Rational Expressions
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8.4: Multiply and Divide Rational Expressions
Example 6 Simplify Step 1: Is there a GCF? Step 2: Factor the numerator(s) (top) into simplest form Step 3: Factor the denominator(s) (bottom) into the simplest form Step 4: Cancel out the factors if needed, multiply and simplify. YES 11/24/2018 5:02 AM 8.4: Multiply and Divide Rational Expressions
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8.4: Multiply and Divide Rational Expressions
Example 7 Simplify 11/24/2018 5:02 AM 8.4: Multiply and Divide Rational Expressions
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8.4: Multiply and Divide Rational Expressions
Your Turn Simplify 11/24/2018 5:02 AM 8.4: Multiply and Divide Rational Expressions
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8.4: Multiply and Divide Rational Expressions
Example 8 Simplify Step 1: Is there a GCF? Step 2: Factor the numerator(s) (top) into simplest form Step 3: Factor the denominator(s) (bottom) into the simplest form Step 4: Cancel out the factors if needed, multiply and simplify. NO 11/24/2018 5:02 AM 8.4: Multiply and Divide Rational Expressions
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8.4: Multiply and Divide Rational Expressions
Example 9 Simplify 11/24/2018 5:02 AM 8.4: Multiply and Divide Rational Expressions
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8.4: Multiply and Divide Rational Expressions
Your Turn Simplify 11/24/2018 5:02 AM 8.4: Multiply and Divide Rational Expressions
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Rules of Divide Expressions
Take GCF of numerator(s) and denominator(s) if possible. Take the reciprocal (flip) of the second fraction. -- KEEP IT, CHANGE IT, FLIP IT -- Factor the numerator(s) (top) into simplest form Factor the denominator(s) (bottom) into the simplest form Cancel out the factors and cancel if needed, multiply and simplify. 11/24/2018 5:02 AM 8.4: Multiply and Divide Rational Expressions
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8.4: Multiply and Divide Rational Expressions
Example 10 Simplify YES Step 1: Is there a GCF? Step 2: Take the reciprocal (flip) of the second fraction. Step 3: Factor the numerator(s) (top) into simplest form Step 4: Factor the denominator(s) (bottom) into the simplest form Step 5: Cancel out the factors if needed, multiply and simplify. 11/24/2018 5:02 AM 8.4: Multiply and Divide Rational Expressions
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8.4: Multiply and Divide Rational Expressions
Example 11 Simplify 11/24/2018 5:02 AM 8.4: Multiply and Divide Rational Expressions
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8.4: Multiply and Divide Rational Expressions
Example 12 Simplify 11/24/2018 5:02 AM 8.4: Multiply and Divide Rational Expressions
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8.4: Multiply and Divide Rational Expressions
Your Turn Simplify 11/24/2018 5:02 AM 8.4: Multiply and Divide Rational Expressions
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8.4: Multiply and Divide Rational Expressions
Assignment Pg all, 7-43 odd (omit 23) 11/24/2018 5:02 AM 8.4: Multiply and Divide Rational Expressions
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