Answer/Discussion on Adding and Subtracting Rational Expressions

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Intermediate Algebra
Answer/Discussion to Practice Problems
on Adding and Subtracting Rational Expressions

Answer/Discussion to 1a

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.

Step 3: Combine 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 Functions.

*Factor the diff. of two squares in the num.

*Divide out the common factor of (x - 5)

(return to problem 1a)

Answer/Discussion to 1b

Step 1: Find the LCD if needed.

The first denominator has the following factors:

*Factor the trinomial

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)

Step 3: Combine 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 Functions.

*Factor out a GCF of -2 in num.

*Divide out the common factor of (a - 3)

(return to problem 1b)

Answer/Discussion to 1c

Step 1: Find the LCD if needed.

The first denominator has the following factor:

The second denominator has the following factors:

*Factor out a GCF of 2

The third denominator has the following factors:

*Factor out a GCF of x

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

Step 3: Combine the rational expressions.

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

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

*Factor the trinomial in num.

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

(return to problem 1c)

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