Question 1066295
What you meant is
1/(x+1)+5x/(x-2)=3 ,
because
1/(x+1)+5x/(x-2) means {{{1/(x+1)+5x/(x-2)}}} ,
but 1/x+1+5x/x-2 means {{{1/x+1+5x/x-2}}} .
 
From {{{1/(x+1)+5x/(x-2)=3}}} ,
we can start by multiplying both sides of the equal sign times {{{(x+1)*(x-2)}}} to get
{{{1*(x+1)*(x-2)/(x+1)+5x*(x+1)*(x-2)/(x-2)=3*(x+1)*(x-2)}}} ,
which simplifies to
{{{x-2+5x*(x+1)=3*(x^2-x-2)}}} ,
{{{x-2+5x^2+5x=3x^2-3x-6}}} .
Adding {{{-3x^2+3x+6}}} to both sides of the equal sign, we get the equivalent equation
{{{2x^2+9x+4=0}}} ,
which we could factor to get
{{{(2x+1)(x+4)=0}}} ,
to find that
either {{{2x+1=0}}} ---> {{{highlight(x=-1/2)}}} ,
or {{{x+4=0}}} ---> {{{highlight(x=-4)}}} .