Question

How do you find the restricted values of x or the rational expression `(x^3-2x^2-8x)/(x^2-4x)`?

Answer 1

`x!=0, 4`

Explanation:

Start by simplifying the equation:

`(x^3-2x^2-8x)/(x^2-4x)`

`=(x(x^2-2x-8))/(x(x-4))`

`=(x(x-4)(x+2))/(color(red)xcolor(blue)((x-4)))`

Recall that any fraction cannot have a denominator of `0`. To find the restrictions for `x`, set each polynomial or term in the denominator to cannot equal to `0`, and solve for `x`.

Finding the restrictions

`1. color(red)x!=0`

`2. color(blue)(x-4)!=0`
`color(white)(ixxxx)x!=4`

`:.`, the restrictions are `x` are `x!=0` and `x!=4`.