Answer:
x+2/x(x+4) or x+2/x^2-4x
Step-by-step explanation:
from the numerator x^2-4x-12, factorise the numerator
x^2-4x-12
multiplying x^2 and -12=-12x^2
step2:
find two numbers that when multiplied you get -12x^2 and when added you get -12x^2.
This numbers are -6x and 2x.
Therefore,(x^2+2x)-(6x-12)
x(x+2)-6(x+2)
(x-6)(x+2)
Step3
from the denominator x^3-x^2+24x, factorise the denominator
x^3-x^2+24x
What is common to all the numbers, the number that is common is x
Therefore,x(x^2-x^2+24x).
multiplying x^2+24x=24x^2
step2:
find two numbers that when multiplied you get 24x^2 and when added you get 24x^2.
This two numbers are -6x and -4x.
Therefore,x{(x^2-4x)-(6x+24)}
x{x(x-4)-6(x-4)}
x{(x-4)(x-6)
Step4
Bringing the nunerator and denominator together.
(x-6)(x+2)/x{(x-4)(x-6)}
(x-6) divides each other
Therefore,x+2/x(x-4) or (x+2)/x^2-4x
