3 6 Title

Intermediate Algebra
Tutorial 33: Adding and Subtracting Rational Expressions

 Step 1: Find the LCD if needed.

 The first denominator has the following factor:

 The second denominator, 5 - x, looks like the first denominator except the signs are switched.  We can rewrite this as

 *Factor out a -1

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

 Note that I did not put the -1 that was in front of the second denominator's (x - 5) factor.  In the step 3, I will put the negative into the problem by placing it in the numerator of that second fraction.

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

 Now the two fractions have a common denominator, so we do not have to rewrite the rational expressions.

 *Combine the two num. *Write over the common den.

 Step 4: Reduce to lowest terms as shown in Tutorial 32: Multiplying and Dividing Rational Expressions.

 *Factor the diff. of two squares in the num.     *Divide out the common factor of (x - 5)

 Step 1: Find the LCD if needed.

 The first denominator has the following factors:

 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, then we do not need to change this fraction.

 *Rewriting denominator in factored form

 Rewriting the second expression with the LCD:

 *Missing the factor of (a - 2) in the den. *Mult. top and bottom by (a - 2)

 *Combine the two num. *Write over the common den.

 Step 4: Reduce to lowest terms, as shown in Tutorial 32: Multiplying and Dividing Rational Expressions.

 *Factor out a GCF of -2 in num.     *Divide out the common factor of (a - 3)

 Step 1: Find the LCD if needed.

 The first denominator has the following factor:

 The second denominator has the following factors:

 The third denominator has the following factors:

 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 factors 2 and x in the den.   *Mult. top and bottom by 2x

 Rewriting the second expression with the LCD:

 *Missing the factor of x in the den. *Mult. top and bottom by x

 Rewriting the third expression with the LCD:

 *Missing the factor of 2 in the den. *Mult. top and bottom by 2

 *Combine the three num. *Write over the common den.

 Step 4: Reduce to lowest terms, as shown in Tutorial 32: Multiplying and Dividing Rational Expressions.

 *Divide out the common factor of (x + 2)

Last revised on July 17, 2011 by Kim Seward.