Question

Simplify the rationsl expression 6x(x+3)(x-2)/3(x-2)(x+9)

Answer 1

The simplified given rational expression is
`(6x(x+3)(x-2))/(3(x-2)(x+9))=(2x^2+6x)/(x+9)`.

Explanation:

Given rational expression is

`(6x(x+3)(x-2))/(3(x-2)(x+9))`

Now to simplify the given rational expression:

`(6x(x+3)(x-2))/(3(x-2)(x+9))=(6x(x+3)(x-2))/(3(x-2)(x+9))`

[In the above expression 6 and 3 cancelled and the result is 2, (x-2) and (x-2) getting cancelled each other]

`=(2x(x+3))/(x+9)`

Now applying distributive property to the above expression

`=(2x^2+6x)/(x+9)`

Therefore
`(6x(x+3)(x-2))/(3(x-2)(x+9))=(2x^2+6x)/(x+9)`

Therefore the simplified given rational expression is
`(6x(x+3)(x-2))/(3(x-2)(x+9))=(2x^2+6x)/(x+9)`