Question

`f(x)=3x-1` and `g(x)=x-2`. How do you solve `(f/g)(x)`?

Answer 1

`x=1/3`

Refer to the explanation for the process.

Explanation:

`f(x)=3x-1`

`g(x)=x-2`

`(f/g)(x)` means to divide the expression for `f(x)` by the expression for `g(x)`.

`(f/g)(x)=(3x-1)/(x-2)`

Set `(f/g)(x)` equal to `0`.

`0=(3x-1)/(x-2)`

Multiply both sides by `(x-2)`.

`0(x-2)=(3x-1)/color(red)cancel(color(black)((x-2)))^1xxcolor(red)cancel(color(black)((x-2)))^1`

Simplify.

`0=3x-1`

Switch sides.

`3x-1=0`

Add `1` to both sides.

`3x=1`

Divide both sides by `3`.

`x=1/3`