Find the restricted values of x for the following rational expression.
x^2 + x + 6/8x^2 − 8x
where is 8x^2-8x = 0?
To find the restricted values of x for the given rational expression, we need to identify the values of x that would make the denominator zero, as a fraction cannot have a denominator of zero.
The expression in the denominator is 8x^2 - 8x.
To determine the values of x that make the denominator zero, we need to set the denominator equal to zero and solve for x:
8x^2 - 8x = 0
Factoring out 8x:
8x(x - 1) = 0
Now, we set each factor equal to zero and solve for x:
1. 8x = 0
Divide both sides by 8:
x = 0
2. x - 1 = 0
Add 1 to both sides:
x = 1
So, the restricted values of x for the given rational expression are x = 0 and x = 1, as they would make the denominator zero.