Question

Make x the subject of the equation, y = [(x+4) / (x-3)] - 6 Please help?

Answer 1

`x=(3y+22)/(y-7)`

Explanation:

Given:
`y=(x+4)/(x-3)-6`
Multiplying throughout by `x-3`

`y(x-3)=x+4-6(x-3)`

`xy-3y=x+4+6x+18`
`xy-3y=7x+22`

`xy-7x=22+3y`
`x(y-7)=22+3y`

`x=(22+3y)/(y-7)`

Rearranging

`x=(3y+22)/(y-7)`

Answer 2

`x=(3y+22)/(y+5)`

Explanation:

`y=(x+4)/(x-3)-6`

`"add 6 to both sides"`

`rArry+6=(x+4)/(x-3)larrcolor(blue)"cross multiply"`

`(y+6)(x-3)=x+4larrcolor(blue)"expand factors on left"`

`xy-3y+6x-18=x+4`

`"collect terms in x on the left"`

`xy+6x-x=4+18+3y`

`rArrxy+5x=22+3y`

`"take out a "color(blue)"common factor of x"`

`x(y+5)=22+3y`

`"divide both sides by "(y+5)`

`rArrx=(3y+22)/(y+5)`