February 11th
February 11th
Adding and Subtracting Rational Expressions With Unlike
Denominators
After studying this lesson, you will be able to:
Add and subtract rational expressions with unlike
denominators.
- Remember that when we add or subtract fractions, we must
have a common denominator before we can add. The same is
true for adding and subtracting rational expressions.
- Once we have a common denominator, we keep the
denominator and we add the numerators. Collect like terms
in the numerator.
- Next, simplify if possible by factoring, canceling,
and/or reducing.
Example 1
Find the lowest common denominator for the set of expressions
or numbers: 4, 10, 20
20 will be the lowest common denominator
Example 2
Find a common denominator for the set of expressions or
numbers: 3, 15, 21
105 will be the lowest common denominator
Example 3
Find a common denominator for the set of expressions or
numbers: x 2, x 3, x 4
to find the lowest common denominator for variables, we use
the highest power of the variable
x 4 will be the lowest common denominator
Example 4
Find a common denominator for the set of expressions or
numbers: y, y 2, y 3
to find the lowest common denominator for variables, we use
the highest power of the variable
y 3 will be the lowest common denominator
Example 5
Find a common denominator for the set of expressions or
numbers: 12x 2 , 20x 2
60x 2 will be the lowest common denominator
Example 6
Find a common denominator for the set of expressions or
numbers: 5x 3, 10x 4, 15x 2,
30x 4 will be the lowest common denominator
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