Question

How do you simplify and find the restrictions for `1/(x+4) -2`?

Answer 1

`-(2x-9)/(x+4)`

Restriction (excluded value) is: `x=-4`

Explanation:

You are not allowed (undefined) to divide by 0 so `x+4 !=0`
means that the excluded value is `x=-4`

To solve this you need to 'force' the - 2 to be something over `x+4`

`color(green)(1/(x+4)-[2xxcolor(red)(1)]`

But 1 = `(x+4)/(x+4)`

`color(green)(1/(x+4)-[2xxcolor(red)((x+4)/(x+4))])`

`color(green)(1/(x+4)-color(white)(.)(2color(red)((x+4)))/(color(red)(x+4)))`

`color(green)((1-2x+8)/(x+4))`

`color(green)((-2x+9)/(x+4))`

But `-2x+9" is the same as "-(2x-9)` giving

`color(green)((-(2x-9))/(+(x+4)) = -(2x-9)/(x+4))`