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

Explanation

To show that the function \( y = \log(1+x) - \frac{2x}{2+x} \) is an increasing function for \( x > -1 \), we need to find the derivative \( y' \) and demonstrate that it is positive throughout the domain.

### Step-by-Step Solution:

1. **Define the function**:
\[ y = \log(1+x) - \frac{2x}{2+x} \]
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