Intermediate Algebra Tutorial 33


Intermediate Algebra
Answer/Discussion to Practice Problems
Tutorial 33: Adding and Subtracting Rational Expressions


WTAMU > Virtual Math Lab > Intermediate Algebra > Tutorial 33: Adding and Subtracting Rational Expressions


 

checkAnswer/Discussion to 1a

problem 1a
 
 

Step 1: Find the LCD if needed.

 
The first denominator has the following factor:

 
ad1a1

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

 
ad1a23

*Factor out a -1

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

 
ad1a3

 
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.

 
ad1a4

 

*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.

 
ad1a5
*Factor the diff. of two squares in the num.
 
 

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

(return to problem 1a)

 


 

checkAnswer/Discussion to 1b

problem 1b
 

Step 1: Find the LCD if needed.

 
The first denominator has the following factors:

 
ad1b1

*Factor the trinomial

 
The second denominator has the following factor:

 
ad1b2

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

 
ad1b3

 
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.

 
ad1b4

 

*Rewriting denominator in factored form

 
 

Rewriting the second expression with the LCD:

 
ad1b5

*Missing the factor of (a - 2) in the den.

*Mult. top and bottom by (a - 2)

 
 
 

Step 3: Combine the rational expressions.

 
ad1b6

 

*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.

 
ad1b7
*Factor out a GCF of -2 in num.
 
 

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

(return to problem 1b)

 


 
 

checkAnswer/Discussion to 1c

problem 1c
 

Step 1: Find the LCD if needed.

 
The first denominator has the following factor:

 
ad1c1

 
The second denominator has the following factors:

 
ad1c2
*Factor out a GCF of 2

 
The third denominator has the following factors:

 
ad1c3
*Factor out a GCF of x

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

 
ad1c4

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

 
Rewriting the first expression with the LCD:

 
ad1c5

*Missing the factors 2 and x in the den.
 

*Mult. top and bottom by 2x
 
 

Rewriting the second expression with the LCD:

 
ad1c6

*Missing the factor of x in the den.

*Mult. top and bottom by x

 
 

Rewriting the third expression with the LCD:

 
ad1c7

*Missing the factor of 2 in the den.

*Mult. top and bottom by 2

 
 

Step 3: Combine the rational expressions.

 
ad1c8

*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.

 
ad1c9

*Factor the trinomial in num.
 
 

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

(return to problem 1c)

 

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WTAMU > Virtual Math Lab >Intermediate Algebra >Tutorial 33: Adding and Subtracting Rational Expressions


Last revised on July 17, 2011 by Kim Seward.
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