$\displaystyle x + \frac{7-2x}{x-2}<= \frac{5x+7}{x-2}$

Solve and express solution as a graph and in interval or set notation.

The solutions are x=0 or x=9. (That's given.)

My work:

he factors I find are x and x-9. Test the factors in the intervals...if their product is - then that interval works. (-inf,0) doesn't work. (0,9) works. (9,inf) doesn't work.

The problem is the interval (-inf,0) works in the original equation.

I'm also confused in general with checking for exceptions, where the function is undefined. Is it done before or after simplifying?