Question

solve for y.
\\(11 - \dfrac{10}{y} = y + 18\\)
if there is more than one solution, separate them with commas.
if there is no solution, click on
o solution\.
\\(y = \\)
no solution \\(\sqrt{\square}\\) \\(\frac{\square}{\square}\\)

Explanation:

Step1: Eliminate denominator, multiply by $y$

Multiply each term by $y$ (where $y
eq 0$):
$$11y - 10 = y^2 + 18y$$

Step2: Rearrange into standard quadratic form

Bring all terms to one side:
$$y^2 + 18y - 11y + 10 = 0$$
$$y^2 + 7y + 10 = 0$$

Step3: Factor the quadratic equation

Find two factors of 10 that sum to 7:
$$(y + 2)(y + 5) = 0$$

Step4: Solve for $y$

Set each factor equal to 0:
$y + 2 = 0 \implies y = -2$
$y + 5 = 0 \implies y = -5$
Verify neither makes original denominator 0.

Answer:

$-2, -5$