Question

Given: X = r + 2, Y = 2r - 9, and Z = r 2 + 17r + 30. Simplify [X · Y - Z] ÷ X.

Answer 1

[x.y - z]/x
= y - z/x
= 2r - 9 - (r^2 + 17r + 30)/(r +2)
= 2r - 9 - (r + 2)(r + 15)/(r +2)
= 2r - 9 - (r + 15)
= r - 24

Answer 2

Given the following:

`X = r+2`

`Y = 2r -9` and

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

Simplify:
`[X.Y-Z] / X`

First simplify:
`X \cdot Y`

`X \cdot Y = (r+2) \cdot (2r-9) = r(2r-9)+2(2r-9)`

The distributive property says that:

`a \cdot (b+c) = a\cdot b+ a\cdot c`

`r(2r-9)+2(2r-9) = 2r^2-9r+4r-18 = 2r^2-5r-18`

∴
`X \cdot Y=2r^2-5r-18`

`X\cdot Y -Z = 2r^2-5r-18 -(r^2+17r+30) =2r^2-5r-18 -r^2-17r- 30`

Combine like terms;

`X\cdot Y -Z =r^2-22r-48=r^2-24r+2r-48 = r(r-24)+2(r-24) = (r+2)(r-24)`

Then;

`(X \cdot Y -Z)/(X) = ( (r+2)(r-24))/(r+2) = r-24`

Therefore, the simplified form of
`[X.Y-Z] / X` is r- 24