Find the positive solution to the equation (x^2+9x+18)/(x^2-9)=10

If we first factorise the top and the bottom of the equation we can see that the top is equal to (x+6)(x+3) and the bottom is (x-3)(x+3). This means we can divide the top and bottom by (x+3) giving us a result of x=-3 which is negative so is not the required solution. However, we are then left with (x+6)/(x-3)=10 which can be rearranged to give (x+6)=10(x-3) and then expanded to give us x+6=10x-30. Rearranging again we get to 9x=36 and then dividing through by 9 we get x=4 which is a positive solution, as required.