Question

How do you simplify and find the restrictions for `3/(x-4)-7`?

Answer 1

Restriction: `color(red)(x!=4)`
Simplification (maybe): `color(blue)((31-7x)/(x-4))`

Explanation:

Since division by `0` is undefined.
`x-4!=0color(white)("xxx")rarrcolor(white)("xxx")x!=4`

What is considered a "simplification" is more problematic.
Here is one possibility:
`color(white)("XXX")3/(x-4)-7`

`color(white)("XXXXXX")=3/(x-4)-(7(x-4))/(x-4)`

`color(white)("XXXXXX")=3/(x-4)-(7x-28)/4`

`color(white)("XXXXXX")=(3-7x+28)/(x-4)`

`color(white)("XXXXXX")=(31-7x)/(x-4)`