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))#