How Do These Algebraic Expressions Equate in an ODE Problem?

[andrew.c]

Homework Statement

I'm doing an ODE problem, and I have a set of solutions for it, but I do not understand how

\frac{y+1}{y-1} = Cx^2

can equal

y = \frac{1+Cx^2}{1-Cx^2}

Many Thanks!

 

[Mark44]

The basic technique is to multiply both sides by y - 1, then move all terms in y to one side and all other terms to the other side and solve for y.

For this problem, though, I get y = (Cx^2 + 1)/(Cx^2 - 1), which is different from what you showed.