I'm differentiating $\displaystyle \frac{\sqrt{1-x^2}}{1-x}$ and coming up with the answer $\displaystyle \frac{1-x}{(1-x^2)(1-x)^\frac{1}{2}}$ and an online differentiator I've run it through gives the same answer. However, the book I'm working from gives the answer as $\displaystyle \frac{1}{(1-x)(1-x^2)^\frac{1}{2}}$.

Which of these is correct? Or are they both the same and I'm just missing a way of simplifying my answer?