Question

Question #d7b37

Answer 1

`(x^2-6)/(12x+9)`

Explanation:

Assumption: the given expression is meant to be:

`(x/3 -2)/(3/x^2+4/x)`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Consider the numerator")`

`x/3-2 -> x/3-6/3 color(blue)(= (x-6)/3)`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Consider the denominator")`

`3/x^2+4/x -> (3x+4x^2)/x^2`
,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Putting it all together")`

`(x-6)/3 -: (3x+4x^2)/x^2`

`(x-6)/3xxx^2/(3x+4x^2) " "=" "(x^3-6x^2)/(12x^2+9x)`

Factor out `x` from top and bottom.

`(cancel(x)^1(x^2-6))/(cancel(x)^1(12x+9))`