# 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.

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