How do we solve rational equations?

          The single thing that complicates solving rational equations is getting that common denominator. Much like adding and subtracting rational expressions the denominators must be the same. Let's take a look at an example:
                                         
        Our common denominator is going to be 5x(x+2) so you have to multiply each part of the equation so that they each have the same denominator. Multiply the first section by 5x, the second by 5(x+2), and the third by x+2. After all of that your new equation will look like this:
                            
             At this point, the denominators are the same. So do they really matter? Not really (other than for saying what values x can't be). So cross out the denominators and you have an equation that looks like: 15x–(5x + 10) =x+2. The rest is cake we are trying to get x alone so you solve like a regular equation. First distribute. Then The rest looks like:
                                      15x – (5x + 10) = x +2
                                          10x – 10 = x + 2
                                                9x = 12 
                                            x = ¹²/₉ = ⁴/₃
                 Since x = ⁴/₃ won't cause any division-by-zero problems in the fractions in the original equation, then this solution is valid. And that's all there is to it!