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

WTAMU > Virtual Math Lab > College Algebra > 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.

(return to problem 1a)

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.

(return to problem 1b)

WTAMU > Virtual Math Lab > College Algebra > Tutorial 9: Multiplying and Dividing Rational Expressions