Final answer:
To simplify the rational expression x^2-x/(x-1)(x+7), factor the numerator to get x(x-1) and then cancel out the (x-1) terms, resulting in x/(x+7). The excluded values are x = 1 and x = -7, which make the denominator zero and thus are not allowed.
Step-by-step explanation:
To simplify the rational expression x^2-x/(x-1)(x+7), we need to factor the numerator and then see if any terms can be canceled with the denominator. Factoring x^2-x we get x(x-1). Now, the expression is x(x-1)/(x-1)(x+7). We can cancel out the (x-1) terms, simplifying the expression to x/(x+7).
The excluded values are values of x that would make the denominator equal to zero because division by zero is undefined. Setting the denominator (x-1)(x+7) to zero, we solve for x to find the excluded values. The solutions are x = 1 and x = -7. These are the values that cannot be used for x in the original expression.