Write as a single fraction \(\frac{1}{1 - x} + \frac{2}{1 + x}\)

Answer Details

To add the fractions \(\frac{1}{1-x}\) and \(\frac{2}{1+x}\), we need to have a common denominator. We can obtain this by multiplying the first fraction by \((1+x)/(1+x)\) and the second fraction by \((1-x)/(1-x)\). This gives us:
$$
\frac{1}{1-x} \cdot \frac{1+x}{1+x} + \frac{2}{1+x} \cdot \frac{1-x}{1-x} = \frac{1+x}{1-x^2} + \frac{2(1-x)}{1-x^2}
$$
Combining the two fractions gives us:
$$
\frac{1+x+2(1-x)}{1-x^2} = \frac{3-x}{1-x^2}
$$
Therefore, the single fraction is \(\boxed{\frac{3-x}{1-x^2}}\).