Question

Simplify: x^2-4x-12/x^3-10x^2+24x

Answer 1

x+2/x(x+4) or x+2/x^2-4x

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

Answer 2

(x + 2) / x(x - 4).

Explanation:

x^2-4x-12/x^3-10x^2+24x

= (x + 2)(x - 6) / x(x^2 - 10x + 24)

= (x + 2)(x - 6) / x(x - 4)(x - 6) x -6 is common to top and bottom so:

= (x + 2) / x(x - 4).