Answer
x does not exist
Work Step by Step
Using proportions, we obtain:
$\frac{x-6}{2-x} = \frac{3}{x+2} \\ x^2 -4x -12 = 6 - 3x \\ x^2 -x - 18 = 0 $
We use the quadratic formula to obtain:
$ x = \frac{1 \pm \sqrt{73}}{2}$
Since RS equals x-6, this value must be greater than 6. However, both solutions are less than 6, so x does not exist.