Solve the equation (6/x-2)-(6/x+1) =1

1 - Multiply each part of equation by denominators to multiply out the fractions. {(6(x-2))/x-2} - {(6(x-2))/x+1} = 1(x-2). This would simply to 6 - {(6(x-2))/x+1} = x - 2. We then do the same for the other denominator. {6(x+1)} - {(6(x-2))/x+1)x+1} = (x-2)(x+1). This would simplify to 6x +6 - 6x + 12 = x^2 - x - 2. 2 - Rearrange quadratic equation to solve for x: x^2 - x - 20. 3 - Factorise. This is done by finding 2 numbers which multiply to equal -20 and add to equal -1. In this case the 2 numbers are -5 and 4. We put these in the brackets like so. (x - 5) (x + 4). An additional step could be to multiply the brackets out to check the equations match, but this would take up time. 4 - Finally, solve for x by making each bracket equal to 0: x - 5 = 0, therefore x = 5 and x+4 = 0, therefore x = -4. Final solutions are are x = 5 and -4.