Question

For what values of x is the rational expression below undefined?

check all that apply

x-4/3x^2-75

A.5
B.4
C.3
D.-3
E.-4
F.-5

Answer 1

Hello,

A fraction is not defined if its denominator is null.

3x²-75=0
==>3(x²-25)=0
==>(x+5)(x-5)=0
==>x=-5 or x=5

Answer 2

Rational expression is undefined for x = -5 and x=5

A and F are correct options.

Explanation:

The ration function is
`(x-4)/(3x^2-75)`

A rational function is undefined when the denominator is zero.

Hence, let us find the value where the expression is undefined by equating denominator equals zero.

`3x^2-75=0\\\\3x^2=75\\\\x^2=25\\\\x=\pm5`

Hence, the rational expression is undefined for x = -5 and x=5

Thus, A and F are correct options.