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
