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.
Prev | Next |