Question #d7b37

1 Answer
Sep 22, 2016

(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))