Answer:
r - 24
Step-by-step explanation:
Use PEMDAS:
P Parentheses first
E Exponents (ie Powers and Square Roots, etc.)
MD Multiplication and Division (left-to-right)
AS Addition and Subtraction (left-to-right)
================================================
[tex]X=r+2,\ Y=2r-9,\ Z=r^2+17r+30[/tex]
[tex][X\cdot Y-Z]\div X[/tex]
First: the product X · Y:
[tex](r+2)(2r-9)[/tex] use FOIL (a + b)(c + d) = ac + ad + bc + bd
[tex]=(r)(2r)+(r)(-9)+(2)(2r)+(2)(-9)\\\\=2r^2-9r+4r-18=2r^2+(-9r+4r)-18\\\\=2r^2-5r-18[/tex]
Second: the difference X · Y - Z:
[tex]2r^2-5r-18-(r^2+17r+30)=2r^2-5r-18-r^2-17r-30\\\\=(2r^2-r^2)+(-5r-17r)+(-18-30)\\\\=r^2-22r-48[/tex]
Third: the quotient [X · Y - Z] ÷ X:
[tex](r^2-22r-48)\div(r+2)=\dfrac{r^2-22r-48}{r+2}=\dfrac{r^2+2r-24r-48}{r+2}\\\\=\dfrac{r(r+2)-24(r+2)}{r+2}=\dfrac{(r+2)(r-24)}{r+2}[/tex]
cancel r + 2
[tex]=r-24[/tex]
