Solve using a graphing calculator $$ -\frac{6}{a-9}+\frac{6}{a-4}=5 $$

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Solve the equation $$ -\frac{6}{a-9}+\frac{6}{a-4}=5 $$.
Solve the equation by following steps:
- step0: Solve for $$a$$:
  $$-\frac{6}{a-9}+\frac{6}{a-4}=5$$
- step1: Find the domain:
  $$-\frac{6}{a-9}+\frac{6}{a-4}=5,a \in \left(-\infty,4ight)\cup \left(4,9ight)\cup \left(9,+\inftyight)$$
- step2: Multiply both sides of the equation by LCD:
  $$\left(-\frac{6}{a-9}+\frac{6}{a-4}ight)\left(a-9ight)\left(a-4ight)=5\left(a-9ight)\left(a-4ight)$$
- step3: Simplify the equation:
  $$-30=5a^{2}-65a+180$$
- step4: Swap the sides:
  $$5a^{2}-65a+180=-30$$
- step5: Move the expression to the left side:
  $$5a^{2}-65a+180-\left(-30ight)=0$$
- step6: Subtract the numbers:
  $$5a^{2}-65a+210=0$$
- step7: Factor the expression:
  $$5\left(a-7ight)\left(a-6ight)=0$$
- step8: Divide the terms:
  $$\left(a-7ight)\left(a-6ight)=0$$
- step9: Separate into possible cases:
  $$\begin{align}&a-7=0\&a-6=0\end{align}$$
- step10: Solve the equation:
  $$\begin{align}&a=7\&a=6\end{align}$$
- step11: Check if the solution is in the defined range:
  $$\begin{align}&a=7\&a=6\end{align},a \in \left(-\infty,4ight)\cup \left(4,9ight)\cup \left(9,+\inftyight)$$
- step12: Find the intersection:
  $$\begin{align}&a=7\&a=6\end{align}$$
- step13: Rewrite:
  $$a_{1}=6,a_{2}=7$$
The solutions to the equation $$ -\frac{6}{a-9}+\frac{6}{a-4}=5 $$ are $$ a=6 $$ and $$ a=7 $$.
The solutions are $$ a=6 $$ and $$ a=7 $$.

Solve using a graphing calculator \( -\frac{6}{a-9}+\frac{6}{a-4}=5 \)

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