Final answer:
The correct answer is option A. The excluded values of x in the given expression are 1 and -7, as these values would cause the denominator to be zero, leading to an undefined expression.
Step-by-step explanation:
To find the excluded values of x for the expression (x² - x) / ((x - 1)(x + 7)), we must identify the values that would make the denominator equal to zero since division by zero is undefined. We can set each factor in the denominator equal to zero and solve for x:
- x - 1 = 0 → x = 1
- x + 7 = 0 → x = -7
Therefore, the excluded values of x are 1 and -7, because if x were equal to either of these values, the denominator of the given expression would be zero, which is not allowed in mathematics.
To find the excluded values of x in the expression, we need to determine the values of x that would make the denominator equal to zero.
The expression has two factors in the denominator: (x - 1) and (x + 7). So, if either of these factors is equal to zero, the whole expression would be undefined.
Setting each factor equal to zero, we get:
x - 1 = 0, which gives x = 1
x + 7 = 0, which gives x = -7
Therefore, the excluded values of x in the expression are x = 1 and x = -7.