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
= [ (r+2) ( 2r-9) - (r^2 + 17r +30)] ÷ (r+2)
= [ r (2r-9) +2 (2r-9) - (r^2 + 17r +30)] ÷ (r+2)
= [ 2r^2 -9r + 4r - 18 - r^2 - 17r - 30] ÷ (r+2)
= [ r^2 -22r - 48] ÷ (r+2)
= (r-24)(r+2) ÷ (r+2)
= r - 24