Question

Rational expressions

(for what value of x is the rational expression below undefined)?
3x-12/9-x ...?

Answer 1

For x = 9 the given rational expression
`(3x-12)/(9-x)` is undefined.

Explanation:

Given rational expression
`(3x-12)/(9-x)`

We have to find for what value of x is the given rational expression is undefined.

Consider the given rational expression
`(3x-12)/(9-x)`

For a fractional expression to be undefined the denominator has to be zero, so that
`(x)/(0)=\infty`

Thus, for the given expression
`(3x-12)/(9-x)`

Denominator is 9-x

Thus, to make it not defined, Put 9 - x = 0

⇒ x = 9

Thus, for x = 9 the given rational expression
`(3x-12)/(9-x)` is undefined.

Answer 2

the answer
3x-12/9-x is undefined if 9-x=0, it means x=9
the value of x=9
proof
3*9 - 12/9-9 = 15/0 (undefined)