Solve each of the following equal $$ \frac{x^{2}-5 x+6}{x^{2}-2}=0 $$

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Solve the equation $$ \frac{x^{2}-5x+6}{x^{2}-2}=0 $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$\frac{x^{2}-5x+6}{x^{2}-2}=0$$
- step1: Find the domain:
  $$\frac{x^{2}-5x+6}{x^{2}-2}=0,x \in \left(-\infty,-\sqrt{2}ight)\cup \left(-\sqrt{2},\sqrt{2}ight)\cup \left(\sqrt{2},+\inftyight)$$
- step2: Cross multiply:
  $$x^{2}-5x+6=\left(x^{2}-2ight)	imes 0$$
- step3: Simplify the equation:
  $$x^{2}-5x+6=0$$
- step4: Factor the expression:
  $$\left(x-3ight)\left(x-2ight)=0$$
- step5: Separate into possible cases:
  $$\begin{align}&x-3=0\&x-2=0\end{align}$$
- step6: Solve the equation:
  $$\begin{align}&x=3\&x=2\end{align}$$
- step7: Check if the solution is in the defined range:
  $$\begin{align}&x=3\&x=2\end{align},x \in \left(-\infty,-\sqrt{2}ight)\cup \left(-\sqrt{2},\sqrt{2}ight)\cup \left(\sqrt{2},+\inftyight)$$
- step8: Find the intersection:
  $$\begin{align}&x=3\&x=2\end{align}$$
- step9: Rewrite:
  $$x_{1}=2,x_{2}=3$$
The solutions to the equation $$\frac{x^{2}-5x+6}{x^{2}-2}=0$$ are $$x=2$$ and $$x=3$$.
The solutions are $$x=2$$ and $$x=3$$.

Solve each of the following equal

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