Differential equation trick?

Question

I have a problem solving the following D.E: $y'=y^2 (t+e^t)$. The solution involves doing $(y')/(y^2) = (-1/y)'$

My question is simply why. How does one note / come to this?

Edit: nevermind, soved. Using the quoticient rule it follows trivially.

Answer 1

$$y'=y^2(t+e^t)\to \frac{dy}{dt}=y^2(t+e^t)\to dy=y^2(t+e^t)dt\to\frac{dy}{y^2}=(t+e^t)dt\to$$$$\int\frac{dy}{y^2}=\int(t+e^t)dt\to-\frac{1}{y}-C=\frac{t^2}{2}+e^t\to y=-\frac{1}{\frac{t^2}{2}+e^t+C}$$