Question
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Tutor-Verified Answer
Answer
The expression is undefined when
, and it simplifies to
.
Solution
Step 1: Determine the values for which the expression is undefined.
The expression is
It is undefined when the denominator is zero. Set the denominator equal to zero:
Solve for
:
Thus, the expression is undefined at
.
Step 2: Simplify the expression.
First, factor the numerator:
The denominator can be factored as:
Now, the expression becomes:
Since
(as determined in Step 1), we can cancel the common factor
:
Final Answers:
-
The expression is undefined when
. -
The simplified expression is
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The Deep Dive
The expression will be undefined where the denominator is equal to zero. For
, solving for
gives
. Thus, the expression is undefined at
.
To simplify the expression
, first factor both the numerator and the denominator. The numerator
factors to
, and the denominator
factors to
. Canceling the common factor of
results in the simplified expression
for
.