ALEKS PURPLE Restriction on a variable in a denominator
ALEKS PURPLE Adding Rational Expressions
Express as a single fraction in lowest terms:
zyzy,,83 ，，264zz
These problems ask you to add algebraic fractions. Algebraic fractions are not much different from regular fractions in the process you use. Find a common denominator, then add the numerators only and reduce your answer:
Let’s look first at the denominators: 6z, 4z, and 1. Each denominator is only one
term—that’s makes it easy. Let’s look at the coefficient first (the number part) of each
denominator:
6, 4, and 1. The LCD of these three numbers is 12 (see below):
6, 12, 18, 24, 30, …
4, 8, 12, 16, 20, …
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, …
Now, let’s look at the variables next:
z and z. The LCD of these variables is z.
Thus, the LCD of the three fractions is 12z.
To change the denominator of the first fraction (6z) to 12z, we must multiply by 2. To change the denominator of the second fraction (4z) to 12z, we must multiply by 3. To change the denominator of the third fraction (1) to 12z, we must multiply by 12z.
What we multiply the denominator by, we must multiply the numerator by the same expression or we will be changing the value of the fraction. Let’s do that step by step:
First fraction:
282(8)216zyzyzy,,,•,,261212zzz
Second fraction:
333(3)39zyzyzy,,,•,,341212zzz
Third fraction:
12224zz•,12112zz
Next, we will rewrite the problem using the three fractions over the common
denominator:
2163924zyzyz,,，，121212zzz
Add only the numerators:
(216)(39)(24)zyzyz,，,，
12z
Note that the parenthesis aren't necessary herewith addition, but they are critical with subtractionso I like to use them all the time. Let's simplifythe numerator by adding & subtracting like terms:(216)(39)(24)zyzyz,，,，
12z
2163924zyzyz,，,，
12z
2925zy,
12z
At this point, be very careful to see if there is
any way to reduce the fraction. Since the numeratorand denominator have no common factors, this isthe answer:
2925zy,
12z
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