Read over each button's application in your calculator's manual. It will prevent any confusion and make solving other problems in the future easier. Reference your actual calculator while your are reading the manual.
Press the capitalized Y button on your calculator.
Plug in one side of the equation to Y1 and the other side to Y2. To stay consistent with the example above, enter (x-2)/(10-x) into Y1 and (3x+3)/(x+1) into Y2. It does not matter which side goes where because each equation is the same value. Press the enter button to save the equations into the calculator.
Graph the rational equation. Press the buttons 2nd and Trace at the same time. When the options are shown, choose option five, which is Intersect. Be sure to consult your manual for brand-specific details if you are having trouble with this step.
Scroll to find the intersection point once the graph comes up. This is your answer to the value of x. For this equation, x should equal 3. The value for x will also appear at the bottom of the screen. You can also zoom in for a closer look at the point of intersection and other points on the graph.