How does: 4/(x+3) - 2/(x+1)^3 + 2/(x+1)^2 + 5/(x+1) turn into 4/(x+3) + (2x)/(x+1)^3 + 5/(x+1)

$$\\ \frac{4}{(x+3)} - \frac{2}{(x+1)^3} + \frac{2}{(x+1)^2} + \frac{5}{(x+1)}\;\; turn \;into\;\frac{ 4}{(x+3)} + \frac{(2x)}{(x+1)^3} + \frac{5}{(x+1)}\\\\
Mmm\\
\frac{4}{(x+3)} - \frac{2}{(x+1)^3} + \frac{2}{(x+1)^2} + \frac{5}{(x+1)}\\\\
=\frac{4}{(x+3)} + \frac{-2}{(x+1)^3} + \frac{2(x+1)}{(x+1)^3} + \frac{5}{(x+1)}\\\\
=\frac{4}{(x+3)} + \frac{-2+2x+2}{(x+1)^3} + \frac{5}{(x+1)}\\\\
=\frac{4}{(x+3)} + \frac{2x}{(x+1)^3} + \frac{5}{(x+1)}\\\\$$

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