From Förberedande kurs i matematik 1

An expression which consists of several fraction signs can be rewritten in terms of one fraction sign by systematically eliminating all partial fractions.

In our expression, we multiply the top and bottom of the main fraction by \displaystyle x+1 (so as to get rid of \displaystyle x+1 from the numerator),

\displaystyle \frac{\,\dfrac{x}{x+1}\,}{3+x} = \frac{\,\dfrac{x}{x+1}\,}{3+x}\cdot\frac{x+1}{x+1} = \frac{\,\dfrac{x}{x+1}\cdot (x+1)\,}{\,(3+x)(x+1)\,} = \frac{x}{(3+x)(x+1)}\,\textrm{.}