Question

solve for y.
\frac{y - 7}{y + 2} + 1 = \frac{y - 5}{y + 3}
if there is more than one solution, separate them with commas.
if there is no solution, click on
o solution\.
y = \square

Explanation:

Step1: Eliminate denominators

Multiply all terms by $(y+2)(y+3)$:
$$(y-7)(y+3) + (y+2)(y+3) = (y-5)(y+2)$$

Step2: Expand all polynomials

$$(y^2 -4y -21) + (y^2 +5y +6) = y^2 -3y -10$$

Step3: Simplify left-hand side

$$2y^2 + y -15 = y^2 -3y -10$$

Step4: Rearrange to standard quadratic form

$$y^2 +4y -5 = 0$$

Step5: Factor the quadratic

$$(y+5)(y-1) = 0$$

Step6: Solve for y, check domain

Exclude $y=-2,-3$ (denominator zeros); solutions are valid.

Answer:

$y = -5, 1$