Question

solve for x.
$4 + \frac{15}{x} = x - \frac{17}{x}$
if there is more than one solution, separate them with commas.
if there is no solution, click on
o solution\.
$x = \square$

Explanation:

Step1: Eliminate denominators

Multiply all terms by $x$ (where $x
eq 0$):
$4x + 15 = x^2 - 17$

Step2: Rearrange to standard quadratic form

Bring all terms to one side:
$x^2 - 4x - 32 = 0$

Step3: Factor the quadratic

Find two factors of -32 that sum to -4:
$(x - 8)(x + 4) = 0$

Step4: Solve for x

Set each factor equal to 0:
$x - 8 = 0 \implies x=8$
$x + 4 = 0 \implies x=-4$
Verify neither makes original denominator 0.

Answer:

$8, -4$