[Tex]\frac{2x}{x^2+1}[\tex] But use / instead of \

Anyway, so we have:

I think.

There are a few ways that you could go about this. I'd start by collecting everything on one side of the equation:

Now, you could, if you wanted to, find a common denominator. The lowest common denominator isn't actually affected by the

though because we can manipulate this to match anything we want. Just look at the algebraic fractions.

is the lowest common denominator for both of them. So I multiply both the numerator and denominator by the missing components, as it were, one at a time.

Hopefully you should be able to see that the parts in red cancel to give us exactly what we had in the stage above. I've multiplied through both the numerator and denominator by the same value, so I haven't changed anything - the denominators are now exactly the same. Can you combine and expand them? You need to rewrite everything as one fraction. You don't need to change the denominators at all.