Question

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

Answer 1

$\frac{3x-12}{x-4} \\ \boxed{x-4 \neq 0 \to \ \ x \neq 4} \\ \\ \frac{3x-12}{x-4} = \frac{3(x-4)}{(x-4)}= 3$

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 :

$R=\dfrac{3x-12}{x-4}.$

We have

$R\\\\\\=\dfrac{3x-12}{x-4}\\\\\\=\dfrac{3(x-4)}{(x-4)}.$

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

$R=\dfrac{3(x-4)}{(x-4)}=3.$

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

Option (B) is CORRECT.