Solving equations that reduce to the form P/Q = 0
We use the fact that, if $\displaystyle \frac{P}{Q}=0$, then $P=0$.
NoteThe expression $\dfrac{P}{Q}$ is not defined if $Q = 0$ so you need to eliminate all solutions that make $Q$ zero.
Examples
1. \t $\displaystyle \frac{x^2-1}{x-2} = 0$
\\ \t $x^2-1=0$ \t
\\ \t $(x-1)(x+1) = 0$ \t
\\ \t $x=-1$ #[or][o]# $x=1$ \t
\\ \\
2. \t $\displaystyle \frac{(x+1)(x+2)^2 - (x+1)^2(x+2)}{(x+1)^4 - (x-2)^2} = 0$
\\ \t $(x+1)(x+2)^2 - (x+1)^2(x+2) = 0$ \t
\\ \t $(x+1)(x+2)[(x+2) - (x+1)] = 0$ \t
\\ \t $(x+1)(x+2)(1) = 0$
\\ \t $x = -1$ #[or][o]# $x = -2$ \t
\\ \\
3. \t $\displaystyle \frac{(x+1)(x+2)^2 - (x+1)^2(x+2)}{x+2} = 0$
\\ \t $(x+1)(x+2)^2 - (x+1)^2(x+2) = 0$ \t
\\ \t $x = -1$ #[or][o]# $x = -2$ \t
\\ \t $x = -1$ \t