For what value of y is the expression \(\frac{y + 2}{y^{2} - 3y - 10}\) undefined?

A.

y = 0

B.

y = 2

C.

y = 3

D.

y = 5

E.

y = 10

Correct answer is D

\(\frac{y + 2}{y^2 - 3y - 10}\) 

\(y^2 - 3y - 10 = 0 \implies y^2 - 5y + 2y - 10 = 0\)

\(y(y - 5) + 2(y - 5) = 0\)

\((y - 5)(y + 2) = 0\)

\(\frac{y + 2}{(y - 5)(y + 2)} = \frac{1}{y - 5}\)

\(\therefore\) At y = 5, the expression \(\frac{y + 2}{y^2 - 3y - 10}\) is undefined.