Question

Given: X = r + 2, Y = 2r - 9, and Z = r 2 + 17r + 30.

Simplify [X · Y - Z] ÷ X.

-r - 24
r - 24
2r2 - 6r - 33
2r2 + 6r + 33

Answer 1

`(r-24)`

Explanation:

`X=r+2`

`Y=2r-9`

`Z=r^2+17r+30`

Let us find

X.Y-Z

`(r+2)(2r-9)-(r^2+17r+30)`

`(2r^2-9r+4r-18)-(r^2+17r+30)`

`2r^2-r^2-5r-17r-18-30`

`r^2-22r-48`

`r^2-24r+2r-48`

`r(r-24)+2(r-24)`

`(r-24)(r+2)`

Now we divide it by X i.e. (r+2)

[X.Y-Z]÷X

`((r-24)(r+2))/((r+2))`

`=(r-24)`