Question

solve for y.
\frac{-7y}{y^{2}-y - 12}-\frac{6}{y - 4}=\frac{y}{y + 3}
if there is more than one solution, separate them with commas.
if there is no solution, click on
o solution\.
\boxed{y = }

Explanation:

Step1: Factor the denominator

First, factor $y^2 - y - 12$:
$y^2 - y - 12 = (y-4)(y+3)$

Step2: Find common denominator

The common denominator is $(y-4)(y+3)$. Multiply each term by it:
$$-7y - 6(y+3) = y(y-4)$$

Step3: Expand all terms

Expand each side of the equation:
$-7y -6y -18 = y^2 -4y$

Step4: Simplify left side

Combine like terms on the left:
$-13y -18 = y^2 -4y$

Step5: Rearrange to standard quadratic

Move all terms to one side:
$y^2 +9y +18 = 0$

Step6: Factor quadratic

Factor the quadratic equation:
$(y+3)(y+6) = 0$

Step7: Identify extraneous solutions

Original equation has restrictions: $y
eq 4, y
eq -3$. So $y=-3$ is invalid.

Answer:

$y = -6$