Solve -1/k^2/frac{2{k^2}+1}

$$\frac { - \frac { 1 } { k ^ { 2 } } } { \frac { 2 } { k ^ { 2 } } + 1 }$$

Evaluate

$$-\frac{1}{k^{2}+2}$$

Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{k^{2}}{k^{2}}.

$$\frac{-\frac{1}{k^{2}}}{\frac{2}{k^{2}}+\frac{k^{2}}{k^{2}}}$$

Since \frac{2}{k^{2}} and \frac{k^{2}}{k^{2}} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{1}{k^{2}}}{\frac{2+k^{2}}{k^{2}}}$$

Divide -\frac{1}{k^{2}} by \frac{2+k^{2}}{k^{2}} by multiplying -\frac{1}{k^{2}} by the reciprocal of \frac{2+k^{2}}{k^{2}}.

$$\frac{\left(-\frac{1}{k^{2}}\right)k^{2}}{2+k^{2}}$$

Cancel out k^{2} and k^{2}.

$$\frac{-1}{2+k^{2}}$$

Differentiate w.r.t. k

$$\frac{2k}{\left(k^{2}+2\right)^{2}}$$