Question

29. Simplify the rational expression state any excluded values 3x-12/x-4

A:X
B:3;where x does not equal 4
C:3;where x does not equal 3
D:0

Answer 1

`(3x-12)/(x-4) \\ \boxed{x-4 \\eq 0 \to \ \ x \\eq 4} \\ \\ (3x-12)/(x-4) = (3(x-4))/((x-4))= 3`

Answer: B:3;where x does not equal 4

Answer 2

Answer: The correct option is

(B) 3; where x does not equal 4.

Step-by-step explanation: We are given to simplify the following rational expression and to state any excluded values that exists :

`R=(3x-12)/(x-4).`

We have

`R\\\\\\=(3x-12)/(x-4)\\\\\\=(3(x-4))/((x-4)).`

Now, if x = 4, then x - 4 = 0, and we cannot divide 0 by 0.

So, let us assume that x ≠ 4, which implies that x - 4 ≠ 0.

Then, we get

`R=(3(x-4))/((x-4))=3.`

Thus, the value of the given rational expression is 3; where x is not equal to 4.

Option (B) is CORRECT.