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Adding and Subtracting Rational Expressions with the Same Denominator

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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