Simplify the rational expression. State any excluded values.
3x minus 12 over x minus 4
A. x
B. 3; where x ≠ 4
C. 3; where x ≠ 3
D. 0
C. 3; where x ≠ 4
Excluded value: x = 4 (since it would make the denominator 0, making the expression undefined)
To simplify the rational expression (3x - 12) / (x - 4), we can factor the numerator if possible.
The numerator (3x - 12) can be factored by taking out the greatest common factor, which is 3. This gives us:
3(x - 4)
Now, the rational expression becomes:
3(x - 4) / (x - 4)
We can see that the factor (x - 4) in both the numerator and denominator can be canceled out, leaving us with:
3
Therefore, the simplified rational expression is 3.
The excluded value in this case is x = 4. This is because if we substitute x = 4 into the original expression, it would make the denominator (x - 4) equal to 0, resulting in an undefined value. So, the excluded value is x = 4.
So, the correct answer is A. x.