Question
Ask by Frank Davey. in Mongolia
Nov 06,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified expression is
.
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Mind Expander
To simplify the expression
, let’s break it down step by step.
First, factor each part of the expression.
-
Numerator of the first fraction:
remains as it is. -
Denominator of the first fraction:
can be checked for factoring, but it does not factor nicely over the reals. -
Numerator of the second fraction:
is a difference of cubes, which can be factored as: -
Denominator of the second fraction:
can be factored as:
Now substituting back into the expression, we have:
Next, we can cancel common factors. Notice that
in the numerator of the second fraction cancels with the denominator of the first fraction, resulting in:
Now we can also cancel
and
(under the condition that
and
):
So, the simplified expression is:
This simplification holds true for all
except when
and
(where the original expression is undefined).