Question

Find all numbers for which the rational expression is undefined: t^3-7t/t^2-64. Please help...

Answer 1

Are you working with real numbers

Answer 2

is this the expression: \(\frac {t^3-7}{t^2-64} \) ??
if so, factor that denominator...
whatever t values make that denominator zero is where the expression itself is undefined.

Answer 3

Recall that you cannot divide by 0, so simply set your denominator equal to 0 and solve when this happens
For example for 1/x I set x=0 so x=0 my rational equation is undefined.
Another example:
1/ t-2 set t-2=0 solve for t
t=2 so you have that t=2 is undefined for your rational equation

Answer 4

Can you recognize what you have in the denominator?
It is a difference of squares (subtracting squares)
(t)^2 - (8)^2 You have for a difference of squares
a^2-b^2=(a+b)(a-b)
So your a=t and b=8
so you have
(t+8)(t-8) so you set this equal to 0
(t+8)(t-8)=0
What does that mean? You have two numbers that when you multiply them you get 0. So that means either one number is equal to 0 or both of them are 0.
That means,
t+8=0 or t-8=0 solve for t in each what do you get?
t=-8 0r t=8 so when t=-8, 8 your rational expression is undefined.