Question 1056723
x^3+2x+3.  Use synthetic division
try -1
-1/1===0==2==3 remember a 0 for the x^2 term.
===1==-1==3==0
the factors are (x+1)(x^2-x+3)=0
x=-1, and by the quadratic formula will give +/- i sqrt(2) for the other 2
{{{graph(300,300,-10,10,-10,10,x^3+2x+3))}}}
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x^4+3X^2-4=0.  Treat this like ax^2+bx+c and factor, only there will be x^2 as leading.
(X^2+4)(X^2-1)=0
x=1,-1,+/-2i
{{{graph(300,300,-10,10,-10,10,x^4+3x^2-4)}}}
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 (x/(x-3)) + (x/(x+3)) = (2/(x^2-9))
Multiply everything by (x^2-9) to clear the fractions.
x(x+3)+x(x-3)=2
x^2+3x+x^2-3x=2
2x^2=2
x^2=1
x=1,-1
Check roots
(1/-2)+(1/4)=2/(-8) works for 1
(1/4)+(-1/2)=2/(-8) works for -1