Question #d7b37

Question

1350 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-09-22T16:16:57

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

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.

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