Find the restricted values of x for the following rational expression.
x^2 + x + 6/8x^2 − 8x
the values to be excluded from the domain are those which make the denominator zero, since division by zero is undefined.
so, where is 8x(x-1) = 0?
To find the restricted values of x for the rational expression (x^2 + x + 6) / (8x^2 - 8x), we need to determine the values of x that would make the denominator equal to zero.
Setting the denominator equal to zero gives us:
8x^2 - 8x = 0
Now, we can factor out 8x from the equation:
8x(x - 1) = 0
By applying the zero-product property, we know that either 8x = 0 or x - 1 = 0.
Simplifying these equations, we find:
1) 8x = 0 -> x = 0
2) x - 1 = 0 -> x = 1
Therefore, the restricted values of x for the given rational expression are x = 0 and x = 1.
To find the restricted values of x in a rational expression, we need to identify the values of x that would make the expression undefined. In a rational expression, the denominator cannot be equal to zero.
In the given expression, the denominator is 8x^2 - 8x. To find the restricted values of x, we need to set the denominator equal to zero and solve for x.
8x^2 - 8x = 0
Factor out the common factor of 8x:
8x(x - 1) = 0
Now, we have two factors: 8x = 0 and (x - 1) = 0
Solving the first factor:
8x = 0
x = 0
Solving the second factor:
x - 1 = 0
x = 1
Therefore, the restricted values of x in the given rational expression are x = 0 and x = 1. These values would make the denominator equal to zero, resulting in an undefined expression.