Rational Expressions

Combining Rational Expressions

EXAMPLE

Perform each operation.

Solution

Factor where possible, then multiply numerators and denominatorsand reduce to lowest terms.

Solution

Factor where possible.

Solution

Use the division property of rational expressions.

Solution

As shown in the list of properties, to subtract two rational expressionsthat have the same denominators, we subtract the numerators whilekeeping the same denominator.

Solution

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 .

Solution

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 equal 1.

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.