Solve for $$ y $$. $$ \frac{y-6}{y-3}=\frac{y+5}{y+3}+1 $$ If there is more than one solution, separate them with commas. If there is no solution, click on "No solution".

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Solve the equation $$ \frac{y-6}{y-3}=\frac{y+5}{y+3}+1 $$.
Solve the equation by following steps:
- step0: Solve for $$y$$:
  $$\frac{y-6}{y-3}=\frac{y+5}{y+3}+1$$
- step1: Find the domain:
  $$\frac{y-6}{y-3}=\frac{y+5}{y+3}+1,y \in \left(-\infty,-3ight)\cup \left(-3,3ight)\cup \left(3,+\inftyight)$$
- step2: Multiply both sides of the equation by LCD:
  $$\frac{y-6}{y-3}	imes \left(y-3ight)\left(y+3ight)=\left(\frac{y+5}{y+3}+1ight)\left(y-3ight)\left(y+3ight)$$
- step3: Simplify the equation:
  $$y\left(y+3ight)-6\left(y+3ight)=2y^{2}+2y-24$$
- step4: Calculate:
  $$y^{2}+3y-6y-18=2y^{2}+2y-24$$
- step5: Simplify:
  $$y^{2}-3y-18=2y^{2}+2y-24$$
- step6: Move the expression to the left side:
  $$y^{2}-3y-18-\left(2y^{2}+2y-24ight)=0$$
- step7: Subtract the terms:
  $$-y^{2}-5y+6=0$$
- step8: Factor the expression:
  $$\left(-y+1ight)\left(y+6ight)=0$$
- step9: Separate into possible cases:
  $$\begin{align}&-y+1=0\&y+6=0\end{align}$$
- step10: Solve the equation:
  $$\begin{align}&y=1\&y=-6\end{align}$$
- step11: Check if the solution is in the defined range:
  $$\begin{align}&y=1\&y=-6\end{align},y \in \left(-\infty,-3ight)\cup \left(-3,3ight)\cup \left(3,+\inftyight)$$
- step12: Find the intersection:
  $$\begin{align}&y=1\&y=-6\end{align}$$
- step13: Rewrite:
  $$y_{1}=-6,y_{2}=1$$
The solutions to the equation $$ \frac{y-6}{y-3}=\frac{y+5}{y+3}+1 $$ are $$ y=-6 $$ and $$ y=1 $$.
The solutions are $$ y=-6 $$ and $$ y=1 $$.

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If there is more than one solution, separate them with commas.
If there is no solution, click on “No solution”.

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Solve for . If there is more than one solution, separate them with commas. If there is no solution, click on “No solution”.