Find the intervals in which the function f(x) = log (1 + x)-x/(1+x), x-1 is increasing or decreasing

f(x)= log(1+x)- x/1+x
Here In log(1+x), 1+x>0 => x>-1
also In x/1+x, 1+x is not equal to 0
=> x is not equal to -1

Now,
f'(x)= 1/(1+x) - ((1+x)-x)/(1+x)^2
= 1/(1+x) - (1+x-x)/(1+x)^2
= 1/(1+x) - 1/(1+x)^2
= x/(1+x)^2

f'(x)>0 iff x/(1+x)^2 > 0
=> x>0
since x is not equal to 0
f'(x) is Strictly Increasing In [0,+ve infinity).

f'(x)=> xsince x is not equal to 0
f'(x) is Strictly Decreasing In (-1,0].

Cheers! :)
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