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
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
\(\frac{y + 2}{y^2 - 3y - 10}\)
\(y^2 - 3y - 10 = 0 \implies y^2 - 5y + 2y - 10 = 0\)
\(y(y - 5) + 2(y - 5) = 0\)
\((y - 5)(y + 2) = 0\)
\(\frac{y + 2}{(y - 5)(y + 2)} = \frac{1}{y - 5}\)
\(\therefore\) At y = 5, the expression \(\frac{y + 2}{y^2 - 3y - 10}\) is undefined.
Source: Myschool Past Questions Archive (Record #22869)