Expert: Bobby Soltani - 7/9/2005

Question
Find the value(s) that makes the expression y^2-16 over
y^2+16 undefined.

Answer
Hi Emma,

This expression becomes undefined when there denominator (bottom) equals zero, because you cannot divide by zero.

The denominator is y^2 + 16, so we need to determine what values of y will make the denominator equal to zero.

y^2 + 16 = 0
y^2 = -16
y = SQRT(-16) and -SQRT(-16)
y = 4i and -4i
where i is SQRT(-1)

We can check our answer:
(4i)^2 + 16 = 0
(4i)(4i) + 16 = 0
16*i^2 + 16 = 0
16*(-1) + 16 = 0
since i^2 = -1
-16 + 16 = 0

You can do the same for -4i.  Let me know if you have any questions.

Bobby