non permissble vaules of this

(6x-24)(x-4) / (x-5)(x^2-2x-10)

1 answer

To find the non-permissible values of a rational function, we need to identify any values of x that would result in a denominator of zero.

In the given expression, the denominators are (x-5) and (x^2-2x-10).

To find the non-permissible values, we set each denominator equal to zero and solve for x:

1) x - 5 = 0
x = 5

2) x^2 - 2x - 10 = 0
This quadratic equation does not factor easily, so we can use the quadratic formula to find the roots:
x = (-(-2) ± √((-2)^2 - 4(1)(-10))) / (2(1))
x = (2 ± √(4 + 40)) / 2
x = (2 ± √44) / 2
x = (2 ± 2√11) / 2
x = 1 ± √11

The non-permissible values for the given rational function are 5, 1 + √11, and 1 - √11.