Title

College Algebra
Answer/Discussion to Practice Problems
Tutorial 9: Multiplying and Dividing Rational Expressions

 Answer/Discussion to 1a

 Step 1: Factor both the numerator and the denominator AND

 Step 2: Write as one fraction.

 *Factor the num. and den.

 In the numerator we factored a  GCF and a trinomial. In the denominator we factored a GCF and a difference of squares.

 Step 3: Simplify the rational expression. AND

 Step 4: Multiply any remaining factors in the numerator and/or denominator.

 *Simplify by div. out the common factors of  x, (x - 1) and (x + 1)       *Multiply the den. out     *Excluded values of the original den.

 Note that the values that would be excluded from the domain are 0, -5, -1, and 1.  Those are the values that makes the original denominator equal to 0.

 Answer/Discussion to 1b

 Step 1: Write as multiplication of the reciprocal AND  Step 2: Multiply the rational expressions as shown above.

 *Rewrite as mult. of reciprocal     *Factor the num. and den.           *Simplify by div. out the common factors of  3, (y^2 + 4), (y - 5), and (y + 2)   *Multiply the den. out       *Excluded values of the original den. of product

 In the numerator of the product we factored a GCF and a trinomial. In the denominator we factored a GCF  and a difference of squares.

 Note that even though all of the factors in the numerator were divided out there is still a 1 in there.  It is easy to think there there is "nothing" left and make the numerator disappear.  But when you divide a factor by itself there is actually a 1 there.  Just like 2/2 = 1 or 5/5 = 1. Note that the values that would be excluded from the domain are 0, 5, -2, and 2.  Those are the values that makes the original denominator of the product equal to 0.

Last revised on Dec. 15, 2009 by Kim Seward.
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