I'm doing some exercises and I came across this one that starts requesting an implicit differentiation of the second derivative:

$\displaystyle x^2a^2+y^2b^2=1$

I've done a few of these implicit differentiation by now but what's confusing me about this one is that the first step of the solutions manual transforms the equation into:

$\displaystyle \frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

Later of course the right side of the equation is set to 0 and x' and y' are calculated. This first step above though has me wondering how the first equation which is a product of x^2a^2 and y^2b^2 gets changed to a division of each respectively looks strange to me. I'm wondering if anyone may have a better understanding of how those might be equivalent?

Thanks in advance...