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Answer
The simplified form is
.
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Mind Expander
To simplify the expression
, let’s start by factoring both the numerator and the denominator.
The numerator
factors as
because
and
are the roots of the quadratic.
Now, let’s factor the denominator
. We can rewrite it as
, and then apply the difference of squares:
.
Putting it all together, we have:
Note that
is the negative of
:
.
Incorporating this fact into our expression, we get:
Final simplified expression: