find the values of t for which the expression is undefined

Question

find the values of t for which the expression is undefined:

(t³ - 9t) / (t(t+3)³)

 

Answer 1

When you're looking for a fraction like this to be undefined, you're trying to make the denominator equal to zero (because we can't divide by 0).

 

So we can do this by examining the bottom of the fraction and trying to think of numbers that would make it equal 0 or we can set it equal to 0 and solve the resulting equation.  

 

Lets try option 2 to be thorough.

 

t(t+3)³ = 0

since it's already factored for us then either t = 0 or...

(t+3)³ = 0   take the cube root of each side

t + 3 = 0     

t = -3

 

so both 0 and -3 make the denominator 0, and thus make the expression undefined.