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To simplify the expression
, we first rewrite the division as multiplication by the reciprocal, giving us:
Next, we need to factor the polynomials.
For the numerator
:
To factor this quadratic, we need two numbers that multiply to -15 and add to -2. Those numbers are -5 and 3, so we can factor it as:
To factor this quadratic, we need two numbers that multiply to -15 and add to -2. Those numbers are -5 and 3, so we can factor it as:
For the denominator
:
This quadratic can be factored by noticing it is a perfect square:
This quadratic can be factored by noticing it is a perfect square:
Now we can substitute back into our expression:
Next, we can cancel the common terms
and
:
After cancellation, we are left with:
Thus, the simplified expression is: