Q:

Basic Alegbra simplification

the sum of x+1 and the reciprocal of x-1 is....???

The answer should be $x^2/(x-1)$. But how this is possible, can anyone explain it? Thanks in advance.

A:

$$x+1+\frac{1}{x-1}=\frac{(x+1)(x-1)+1}{x-1}=\frac{x^2-1+1}{x-1}=\frac{x^2}{x-1}$$

