Combining Rational Expressions
Perform each operation.
Factor where possible, then multiply numerators and
denominatorsand reduce to lowest terms.
Factor where possible.
Use the division property of rational expressions.
As shown in the list of properties, to subtract two rational
expressionsthat have the same denominators, we subtract the
numerators whilekeeping the same denominator.
These three fractions cannot be added until their denominators
arethe same. A common denominator into which p , 2p , and 3p all
divide is 6p. Note that 12p is also a common denominator, but 6p
is the least common denominator.Use the fundamental property to
rewrite each rational expressionwith a denominator of 6p .
To find the least common denominator, first factor each
denominator.Then change each fraction so they all have the same
denominator, being carefulto multiply only by quotients that
Because the numerator cannot be factored further, we leave our
answer in thisform. We could also multiply out the denominator,
but factored form is usuallymore useful.