Show that `y=log(1+x)-(2x)/(2+x),\ x >-1` is an increasing function of `x` throughout its domain.

Explanation

`y=log(x+1)-(2x)/(x+2)`

`dy/dx=1/(1+x)-(2(2+x)-2x)/(2+x)^2`

`impliesdy/dx=(x^2+4+4x-4-4x)/((x+2)^2(x+1))`

for increasing function `dy/dx>0`

implies `x^2/((x+2)^2(x+1))>0impliesx+1>0impliesx>(-1)`

for `x>(-1)` the given function is always increasing.