Question
Reselue into partial fraction
Ask by Weston Fuentes. in Turks and Caicos Islands
Dec 06,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
The partial fraction decomposition of
is
.
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To resolve
into partial fractions, we first factor the quadratic in the denominator. The expression
can be factored as
. Thus, we rewrite the expression as:
Next, we set up the partial fraction decomposition:
Multiplying both sides by the common denominator
leads to:
Now, we can expand and collect terms to solve for the coefficients
and
. After substituting convenient values for
to solve for these coefficients:
- Set
: so . - Set
: so . - Set
: so .
Thus, we find
, leading to the partial fraction decomposition: