Question

Solve the equation. Check the solution. Use a graphing calculator.

Answer 1

Solution

We solve the equation

$\begin{gathered} \frac{3}{x+3}+\frac{6}{x-3}=3 \\ \\ Divide\text{ through by 3} \\ \\ \frac{1}{x+3}+\frac{2}{x-3}=1 \\ \\ Clearing\text{ fraction} \\ \\ x-3+2x+6=x^2-9 \\ 3x+3=x^2-9 \\ \\ x^2-3x-12=0 \end{gathered}$

We now solve the quadratic equation

$\begin{gathered} x^2-3x-12=0 \\ \\ Using\text{ formula method} \\ \\ x=\frac{3\pm\sqrt{3^2-4(1)(-12)}}{2} \\ \\ x=\frac{3\pm\sqrt{9+48}}{2} \\ \\ x=\frac{3\pm\sqrt{57}}{2} \\ \\ Therefore,\text{ the two answers are given below and corrected to two decimal places} \\ \\ x=5.27 \\ and \\ x=-2.27 \end{gathered}$

The graph is given below