4) Solve fot tx tho follo wing equation $$ \frac{x}{x+5}+\frac{x-2}{3-x}+1=0 $$

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Solve the equation $$ \frac{x}{x+5}+\frac{x-2}{3-x}+1=0 $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$\frac{x}{x+5}+\frac{x-2}{3-x}+1=0$$
- step1: Find the domain:
  $$\frac{x}{x+5}+\frac{x-2}{3-x}+1=0,x \in \left(-\infty,-5ight)\cup \left(-5,3ight)\cup \left(3,+\inftyight)$$
- step2: Multiply both sides of the equation by LCD:
  $$\left(\frac{x}{x+5}+\frac{x-2}{3-x}+1ight)\left(x+5ight)\left(3-xight)=0	imes \left(x+5ight)\left(3-xight)$$
- step3: Simplify the equation:
  $$4x-x^{2}+5=0$$
- step4: Factor the expression:
  $$\left(-x+5ight)\left(x+1ight)=0$$
- step5: Separate into possible cases:
  $$\begin{align}&-x+5=0\&x+1=0\end{align}$$
- step6: Solve the equation:
  $$\begin{align}&x=5\&x=-1\end{align}$$
- step7: Check if the solution is in the defined range:
  $$\begin{align}&x=5\&x=-1\end{align},x \in \left(-\infty,-5ight)\cup \left(-5,3ight)\cup \left(3,+\inftyight)$$
- step8: Find the intersection:
  $$\begin{align}&x=5\&x=-1\end{align}$$
- step9: Rewrite:
  $$x_{1}=-1,x_{2}=5$$
The solutions to the equation $$ \frac{x}{x+5}+\frac{x-2}{3-x}+1=0 $$ are $$ x = -1 $$ and $$ x = 5 $$.
The solutions are $$ x = -1 $$ and $$ x = 5 $$.

Solve fot tx tho follo wing equation

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