Multiplying and Dividing Expressions

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Multiplying and Dividing Expressions Section 11.1 © 2012, viet.j.dang@lonestar.edu

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

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

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

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

8.4: Multiply and Divide Rational Expressions Example 2 Simplify 11/24/2018 5:02 AM 8.4: Multiply and Divide Rational Expressions

8.4: Multiply and Divide Rational Expressions Your Turn Simplify 11/24/2018 5:02 AM 8.4: Multiply and Divide Rational Expressions

8.4: Multiply and Divide Rational Expressions Example 3 Simplify 11/24/2018 5:02 AM 8.4: Multiply and Divide Rational Expressions

8.4: Multiply and Divide Rational Expressions Your Turn Simplify 11/24/2018 5:02 AM 8.4: Multiply and Divide Rational Expressions

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

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

8.4: Multiply and Divide Rational Expressions Example 4 Simplify 11/24/2018 5:02 AM 8.4: Multiply and Divide Rational Expressions

8.4: Multiply and Divide Rational Expressions Example 5 Simplify 11/24/2018 5:02 AM 8.4: Multiply and Divide Rational Expressions

8.4: Multiply and Divide Rational Expressions Your Turn Simplify 11/24/2018 5:02 AM 8.4: Multiply and Divide Rational Expressions

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

8.4: Multiply and Divide Rational Expressions Example 7 Simplify 11/24/2018 5:02 AM 8.4: Multiply and Divide Rational Expressions

8.4: Multiply and Divide Rational Expressions Your Turn Simplify 11/24/2018 5:02 AM 8.4: Multiply and Divide Rational Expressions

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

8.4: Multiply and Divide Rational Expressions Example 9 Simplify 11/24/2018 5:02 AM 8.4: Multiply and Divide Rational Expressions

8.4: Multiply and Divide Rational Expressions Your Turn Simplify 11/24/2018 5:02 AM 8.4: Multiply and Divide Rational Expressions

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

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

8.4: Multiply and Divide Rational Expressions Example 11 Simplify 11/24/2018 5:02 AM 8.4: Multiply and Divide Rational Expressions

8.4: Multiply and Divide Rational Expressions Example 12 Simplify 11/24/2018 5:02 AM 8.4: Multiply and Divide Rational Expressions

8.4: Multiply and Divide Rational Expressions Your Turn Simplify 11/24/2018 5:02 AM 8.4: Multiply and Divide Rational Expressions

8.4: Multiply and Divide Rational Expressions Assignment Pg 577 3-5 all, 7-43 odd (omit 23) 11/24/2018 5:02 AM 8.4: Multiply and Divide Rational Expressions