How to decompose the below fraction into sum of 2 terms.

[JayKo]

as below, my math is getting rusty, hope some can help me out.

thanks.

$$\frac{1}{1+\frac{1}{x}}$$

 

[statdad]

First convert it into an ordinary rational expression (try simplifying

$$\frac x{x\left(1 + \dfrac 1 x\right)}$$

then split the result into a sum of two pieces.

Alternately, notice that $1 = 1 + \frac 1 x - \frac 1 x$ and use that in the numerator.