Solving equation with fraction I don't understand how to get from the second to the third step in this equation:
$  - \frac { \sqrt { 2 - x ^ { 2 } } - x \left( \frac { - x } { \sqrt { 2 - x ^ { 2 } } } \right) } { \left( \sqrt { 2 - x ^ { 2 } } \right) ^ { 2 } } = - \frac { \sqrt { 2 - x ^ { 2 } } + \frac { x ^ { 2 } } { \sqrt { 2 - x ^ { 2 } } } } { \left( \sqrt { 2 - x ^ { 2 } } \right) ^ { 2 } } = - \frac { \frac { 2 - x ^ { 2 } } { \sqrt { 2 - x ^ { 2 } } } + \frac { x ^ { 2 } } { \sqrt { 2 - x ^ { 2 } } } } { \left( \sqrt { 2 - x ^ { 2 } } \right) ^ { 2 } } = - \frac { 2 } { \left( \sqrt { 2 - x ^ { 2 } } \right) ^ { 3 } } $
Why can we just add $ 2 - x ^ { 2 } $ in the numerator?
Step 1 to step 2, as well as step 3 to step 4 is clear to me.

It's simply that for $a>0$, $$\sqrt{a} = \sqrt{a}\cdot\underbrace{\left(\frac{\sqrt{a}}{\sqrt{a}}\right)}_1$$
$$=\frac{\sqrt{a}\cdot\sqrt{a}}{\sqrt{a}}$$
$$=\frac{(\sqrt{a})^2}{\sqrt{a}}$$
$$=\frac{a}{\sqrt{a}}$$
In your case, "$a$" is $2-x^2$.
