Question

Solve x/x+1 < x/x-1

Answer 1

You multiply both sides of the equation by (x+1). This makes it x < x / (x-1)(x+1). You then expand the brackets on the right side to make x / x^2 -1. You then split it into two fractions so x/x^2 and x/-1. Then the x/x^2 can also be written as x times x^-2 which equals x^-1. You now have the equation x < x^-1 + x/-1 you now divide both sides by -1 to get -x < -x^-1 + x. Now you add x^-1 to both sides to get x^-1 - x < x. Now you take x from both sides to get x^-1 - 2x < 0. You can now put it make into 1/x - 2x < 0.