Question 44251
{{{1/(3x+6) +2 = 3/(x+2)}}}
We want to find out what the value of x is, but this is very hard when x is in a denominator. We can manipulate the expression by multiplyin by (3x+6):
{{{1 +2(3x+6) = 3(3x+6)/(x+2)}}}
And then multiplying by (x+2):
{{{(x+2) +2(3x+6)(x+2) = 3(3x+6)}}}
Now expand the brackets:
{{{x+2 +2(3x^2+9x+12) = 9x+18)}}}
{{{x+2+6x^2+27x+36=9x+18}}}
{{{6x^2+28x+38=9x+18}}}
Now rearrange so you have zero on the right hand side:
{{{6x^2+19x+20=0}}}
Now you can use the quadratic solver {{{x = (-b +- sqrt( b^2-4ac ))/(2a) }}} 
where
a=6
b=19
c=20
And hopefully get the two congutate roots {{{x=-19/6-(sqrt(199)i)/6}}} or {{{x=-19/6+(sqrt(199)i)/6}}}  
Where "i" denotes the imaginary number {{{i=sqrt(-1)}}}
I hope this helps.
P.S. I am trying to start up my own homework help website. I would be extremely grateful if you would e-mail me some feedback on the help you received to adam.chapman@student.manchester.ac.uk