Question

For what values of x is the rational expression below undefined? x+5/3x^2-3

Answer 1

Undefined at the x- intercepts, +1 and -1. (apex)

Answer 2

Hence, the values of x for which the expression is not defined is equal to 1 or -1.

Explanation:

We are asked to find for which values of x is the rational expression:

`(x+5)/(3x^2-3)` is undefined.

We know that a rational expression is undefined when the denominator term is equal to zero.

Hence, we could represent the algebraic expression as:

`(x+5)/(3x^2-3)=(x+5)/(3(x^2-1))\\\\(x+5)/(3x^2-3)=(x+5)/(3(x-1)(x+1))`

Hence, clearly from the expression we could observe that:

the expression is not defined when x=1 or x=-1.

( since the denominator will be zero if x receives any of the above two values or both)

Hence, the values of x for which the expression is not defined is equal to 1 or -1.