Math Problem Help :'(?

Question

I am stuck on this math problem >_< please help me, how do I solve this math problem

2x/x-1 + x+1/x
________________
4x/x+1 - 2x+2/3x

So confused, I need to make sure I know how to do this problem before I take a math test, someone help fast

Answer 1

2x/x-1 + x+1/x
________________
4x/x+1 - 2x+2/3x

[2x/(x-1) +(x+1)/x]/[4x/(x+1) -(2x+2)/(3x)] <-- You mean this?
=[2x^2+x^2-1]/(x(x-1))/[(12x^2-2x^2-4x-2)/(3x(x+1)]
= (3x^2-1)/(x(x-1)) * (3x(x+1))/(10x^2-4x-2)
= 3(x+1)(3x^2-1)/[(x-1)(10x^2-4x-2)]

Answer 2

You need some brackets:
I assume it is [2x/(x-1) + (x+1)/x]/[4x/(x+1) - (2x+2)/3x]

If it is that, you proceed just as you would with number fractions:

Top is [2x*x +(x-1)(x+1)]/(x-1)*x
Bottom is [12 x*x - 2(x -1)*(x+1)]/3x(x+1)

These are both fractions p/q and r/s;
when you divide them the rule is to calculate p/q*s/r.

So, you want ps/qr.