Adding and Subtracting Rational Expressions with the Same Denominator

EXAMPLE 6

Subtracting Rational Expressions when
Denominators Are Opposites

Subtract:

SOLUTION We note that and are opposites. We multiply
the second rational expression by .

	Multiply the numerator and denominator by -1 by changing every term’s sign.
	Write the numerator and the denominator in descending powers of x .

We now return to the original subtraction problem.

	This is the given problem.
	Replace the second rational expression by the form obtained through multiplication by .
	Subtract numerators. Place this difference over the common denominator . Don’t forget parentheses !
	Remove parentheses and then change the sign of each term .
	Combine like terms in the numerator. Although the numerator can be factored , further simplification is not possible .

CHECK POINT 6 Subtract:.

7.3 EXERCISE SET

Practice Exercises

In Exercises 1–38, add or subtract as indicated. Simplify the result,
if possible.