2/X+3 + 3/X-4=0
2(x-4)+3(x+3)=0
2x-8+3x+9=0
5x=-1
x=-1/5
a-b/2(a+b) - a^2+b^2/a^2-b^2
=(a-b)²/2(a+b) -2(a²+b²)/2(a²-b²)
=(-a²-2ab-b²)/2(a²-b²)
=-(a+b)²/2(a²-b²)
=-(a+b)/2(a-b)
1/x-1 - x^2+2x/x^3-1
=1/(x-1)-(x²+2x)/(x-1)(x²+x+1)
=(x²+x+1-x²-2x)/(x-1)(x²+x+1)
=(1-x)/(x-1)(x²+x+1)
=-1/(x²+x+1)