Question

How do you combine `2/x + 1/(x-2) + 3/(x-2)^2`?

Answer 1

The final denominator should be the simplest form of `x(x-2)^2`, which the written expression is. Just multiply by a form of `1` that gives the correct denominator.

`= 2/x*((x-2)^2)/((x-2)^2) + 1/(x-2)*(x(x-2))/(x(x-2)) + 3/(x-2)^2 * x/x`

`= (2(x-2)^2)/(x(x-2)^2) + (x(x-2))/(x(x-2)^2) + (3x)/(x(x-2)^2)`

`= (2(x-2)^2 + x(x-2) + 3x)/(x(x-2)^2)`