Question

question

divide: \frac{y^2 + y - 42}{y^2 - 36}.

provide your answer below:

Explanation:

Factor the numerator trinomial

Using the Factoring Trinomials knowledge point

$$ y^2 + y - 42 = (y + 7)(y - 6) $$

Factor the denominator binomial

Using the Difference of Squares knowledge point

$$ y^2 - 36 = (y - 6)(y + 6) $$

Simplify the rational expression

We divide the factored numerator by the factored denominator and cancel the common factor:

$$ \frac{y^2 + y - 42}{y^2 - 36} = \frac{(y + 7)(y - 6)}{(y + 6)(y - 6)} = \frac{y + 7}{y + 6} \quad (y eq 6) $$

Answer:

Divide: \(\frac{y^2 + y - 42}{y^2 - 36}\).

Provide your answer below:
<blank>\(\frac{y + 7}{y + 6}\)</blank>