How do you solve #2/(x-1) - 2/3 =4/(x+1)#?
Lots of ways to solve this. All of them work! Here's one way.
Divide both sides of the equation by 2.
Put the two terms on the left-hand side of the equation under a common denominator.
Simplify the numerator of the left-hand side.
Invert both sides of the equation.
Multiply both sides of the equation by
Expand both sides of the equation using the distributive property.
Put this quadratic equation in standard form.
The left-hand side of this equation factors nicely.
I bet you can come up with another way to solve this. What I like about THIS way is that you don't have to deal with quadratics AND quotients in the same equation.