Adding and Subtracting Rational Expressions with Different Denominators
To add or subtract rational expressions with different denominators, we must build
up each rational expression to equivalent forms with identical denominators. Of course, it is most efficient to use the LCD as in the following
examples.
Example 1
Different denominators
Perform the indicated operations.
Solution
a) The LCD for a^{2}b and ab3 is a^{2}b^{3}. To build up each denominator to a^{2}b^{3}, multiply
the numerator and denominator of the first expression by b^{2}, and multiply
the numerator and denominator of the second expression by a:


Build up each denominator to the LCD. 





Add the numerators. 


Build up each denominator
to the LCD 12. 


Distributive property 


Subtract the numerators. Note that 6x  9 is put in
parentheses. 


Remove the parentheses. 


Combine like terms. 
Caution
Before you add or subtract rational expressions, they must
be written with identical denominators. For multiplication and division it is not
necessary to have identical denominators.
