<s>[INST] What are the solutions to: $x(x-3)=x^2 -4$? What are the solutions to: $x(x-3)=x^2 -4$ ?
Subtracting $x^2$ from both side results in the loss of the solution $(x=\infty)$.
My book says the solutions are $(x=\frac{4}{3},\infty)$
But is $(x=-\infty)$ another solution?
Is the answer $(x=\frac{4}{3},\pm\infty)$ or $(x=\frac{4}{3},\infty)$ ?
 [/INST] $$\begin{align}
x(x-3)&=x^2 -4 \\ \\
\iff x^2-3x &= x^2 - 4\\ \\\iff 3x-4&=0\\ \\ \iff 3x&=4 \\ \\ \iff x &= \frac 43
\end{align}$$
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