Question

What is the solution to the equation StartFraction y Over y minus 4 EndFraction minus StartFraction 4 Over y + 4 EndFraction = StartFraction 32 Over y squared minus 16 EndFraction?
y = –4 and y = 4
y = 0
all real numbers
no solution

Answer 1

Domain: y ≠ 4, y ≠ −4. Combine the left-hand side over common denominator (y−4)(y+4):

(y(y+4) − 4(y−4)) / (y^2 − 16) = (y^2 + 16)/(y^2 − 16).

Set equal to 32/(y^2 − 16) and multiply both sides by y^2 − 16 (nonzero):

y^2 + 16 = 32 ⇒ y^2 = 16 ⇒ y = ±4.

Both solutions are excluded by the domain (they make denominators zero), so there is no valid solution. Answer: no solution.