Solve =k/k-2+1/k-6

$$= \frac { k } { k - 2 } + \frac { 1 } { k - 6 }$$

Evaluate

$$\frac{k^{2}-5k-2}{\left(k-6\right)\left(k-2\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of k-2 and k-6 is \left(k-6\right)\left(k-2\right). Multiply \frac{k}{k-2} times \frac{k-6}{k-6}. Multiply \frac{1}{k-6} times \frac{k-2}{k-2}.

$$\frac{k\left(k-6\right)}{\left(k-6\right)\left(k-2\right)}+\frac{k-2}{\left(k-6\right)\left(k-2\right)}$$

Since \frac{k\left(k-6\right)}{\left(k-6\right)\left(k-2\right)} and \frac{k-2}{\left(k-6\right)\left(k-2\right)} have the same denominator, add them by adding their numerators.

$$\frac{k\left(k-6\right)+k-2}{\left(k-6\right)\left(k-2\right)}$$

Do the multiplications in k\left(k-6\right)+k-2.

$$\frac{k^{2}-6k+k-2}{\left(k-6\right)\left(k-2\right)}$$

Combine like terms in k^{2}-6k+k-2.

$$\frac{k^{2}-5k-2}{\left(k-6\right)\left(k-2\right)}$$

Expand \left(k-6\right)\left(k-2\right).

$$\frac{k^{2}-5k-2}{k^{2}-8k+12}$$

Differentiate w.r.t. k

$$\frac{-3k^{2}+28k-76}{\left(\left(k-6\right)\left(k-2\right)\right)^{2}}$$