Simplify the rational expression. State any excluded values.
4x – 4 over x – 1
A. x
B. 4; where xdoes not equal4
C. 0
D. 4; where xdoes not equal1
D. 4; where x does not equal 1
Excluded value: x = 1, because it would make the denominator 0, which is not allowed in a fraction.
To simplify the rational expression (4x - 4)/(x - 1), we can factor the numerator if possible and then cancel out any common factors.
The numerator (4x - 4) can be factored as 4(x - 1).
Now we can rewrite the expression as 4(x - 1)/(x - 1).
The (x - 1) in the numerator and denominator can be canceled out, as long as x ≠ 1 because dividing by zero is undefined. The simplified expression is 4.
Therefore, the correct answer is D. 4; where x does not equal 1.