Simplify, then apply the rules of limit to evaluate

Question

lim x3-5x2+6x/x2-9
x->3

Answer 1

first, we simplify the function:
(x^3-5x^2+6x)/(x^2-9)
x(x^2-5x+6)/(x-3)(x+3)
x(x-2)(x-3)/(x-3)(x+3)
cancel out x-3:
x(x-2)/(x+3)
thus, the limit as x--> is:
3(3-2)/(3+3)
1/2

so there,, :)

Answer 2

Given two functions as:
f(x) = x2-x-1 and g(x) = 3/x
Find fog(x) also find the domain of f, g and fog

Solve the two sided inequality and show the solution on real line
7 < 1-2x ≤ 10