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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