Question

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

Answer 1

We solve the equation

`\begin{gathered} (3)/(x+3)+(6)/(x-3)=3 \\ \\ Divide\text{ through by 3} \\ \\ (1)/(x+3)+(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=(3\pm√(3^2-4(1)(-12)))/(2) \\ \\ x=(3\pm√(9+48))/(2) \\ \\ x=(3\pm√(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