Solve by graphing: $$ \frac{x+9}{2 x}=x+2 $$ $$ \left\{-\frac{3}{2}, 3\right\} $$ $$ \left\{-3, \frac{3}{2}\right\} $$ $$ \{-3,2\} $$ (-3)

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Solve the equation $$ \frac{x+9}{2x}=x+2 $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$\frac{x+9}{2x}=x+2$$
- step1: Find the domain:
  $$\frac{x+9}{2x}=x+2,x
eq 0$$
- step2: Multiply both sides of the equation by LCD:
  $$\frac{x+9}{2x}	imes 2x=\left(x+2ight)	imes 2x$$
- step3: Simplify the equation:
  $$x+9=2x^{2}+4x$$
- step4: Move the expression to the left side:
  $$x+9-\left(2x^{2}+4xight)=0$$
- step5: Calculate:
  $$-3x+9-2x^{2}=0$$
- step6: Factor the expression:
  $$\left(3+xight)\left(3-2xight)=0$$
- step7: Separate into possible cases:
  $$\begin{align}&3+x=0\&3-2x=0\end{align}$$
- step8: Solve the equation:
  $$\begin{align}&x=-3\&x=\frac{3}{2}\end{align}$$
- step9: Check if the solution is in the defined range:
  $$\begin{align}&x=-3\&x=\frac{3}{2}\end{align},x
eq 0$$
- step10: Find the intersection:
  $$\begin{align}&x=-3\&x=\frac{3}{2}\end{align}$$
- step11: Rewrite:
  $$x_{1}=-3,x_{2}=\frac{3}{2}$$
The solutions to the equation $$ \frac{x+9}{2x}=x+2 $$ are $$ x = -3 $$ and $$ x = \frac{3}{2} $$.

Therefore, the solutions are $$ x = -3 $$ and $$ x = \frac{3}{2} $$, which corresponds to the option $$ \{-3, \frac{3}{2}\} $$.
The solutions are $$ x = -3 $$ and $$ x = \frac{3}{2} $$.

Solve by graphing:

(-3)

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Solve by graphing: (-3)