College Algebra Tutorial 10

College Algebra
Answer/Discussion to Practice Problems
Tutorial 10: Adding and Subtracting Rational Expressions

WTAMU > Virtual Math Lab > College Algebra > Tutorial 10: Adding and Subtracting Rational Expressions

Answer/Discussion to 1a

Step 1: Find the LCD as shown in tutorial 10.

The first denominator has the following two factors:

*Factor the trinomial

The second denominator has the following two factors:

*Factor the trinomial

Putting all the different factors together and using the highest exponent, we get the following LCD:

Step 2: Write equivalent fractions using the LCD if needed.

Rewriting the first expression with the LCD:

*Missing the factor of (a + 7) in the den.
*Mult. top and bottom by (a + 7)

Rewriting the second expression with the LCD:

*Missing the factor of (a + 9) in the den.
*Mult. top and bottom by (a + 9)

Step 3: Combine the rational expressions as shown in tutorial 10.

*Combine the numerators
*Write over common denominator

Step 4: Reduce to lowest terms.

This rational expression cannot be simplified down any farther.

Also note that the values that would be excluded from the domain are -9, -3 and -7. These are the values that make the original denominator equal to 0.

(return to problem 1a)

Answer/Discussion to 1b

Step 1: Find the LCD as shown in tutorial 10 if needed.

The first denominator has the following two factors:

*Factor the difference of squares

The second denominator has the following factor:

Putting all the different factors together and using the highest exponent, we get the following LCD:

Step 2: Write equivalent fractions using the LCD if needed.

Since the first rational expression already has the LCD, we do not need to change this fraction.

*Rewriting denominator in factored form

Rewriting the second expression with the LCD:

*Missing the factor of (x - 7) in the den.
*Mult. top and bottom by (x - 7)

Step 3: Combine the rational expressions as shown in tutorial 10.

*Combine the numerators
*Write over common denominator

*Distribute the minus sign through the ( )

Step 4: Reduce to lowest terms.

This rational expression cannot be simplified down any farther.

Also note that the values that would be excluded from the domain are -7 and 7. These are the values that make the original denominator equal to 0.

(return to problem 1b)

WTAMU > Virtual Math Lab > College Algebra > Tutorial 10: Adding and Subtracting Rational Expressions