Simplify the following:
z^2+2 z-6 z-15+9/z^2
Put each term in z^2+2 z-6 z-15+9/z^2 over the common denominator z^2: z^2+2 z-6 z-15+9/z^2 = z^4/z^2+(2 z^3)/z^2-(6 z^3)/z^2-(15 z^2)/z^2+9/z^2:
z^4/z^2+(2 z^3)/z^2-(6 z^3)/z^2-(15 z^2)/z^2+9/z^2
z^4/z^2+(2 z^3)/z^2-(6 z^3)/z^2-(15 z^2)/z^2+9/z^2 = (z^4+2 z^3-6 z^3-15 z^2+9)/z^2:
(z^4+2 z^3-6 z^3-15 z^2+9)/z^2
Grouping like terms, z^4+2 z^3-6 z^3-15 z^2+9 = z^4+(-6 z^3+2 z^3)-15 z^2+9:
(z^4+(-6 z^3+2 z^3)-15 z^2+9)/z^2
2 z^3-6 z^3 = -4 z^3:
Answer: |
| (z^4+-4z^3-15z^2+9)/z^2
