Solve =5k/k+2+2/k

$$= \frac { 5 k } { k + 2 } + \frac { 2 } { k }$$

Evaluate

$$\frac{5k^{2}+2k+4}{k\left(k+2\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of k+2 and k is k\left(k+2\right). Multiply \frac{5k}{k+2} times \frac{k}{k}. Multiply \frac{2}{k} times \frac{k+2}{k+2}.

$$\frac{5kk}{k\left(k+2\right)}+\frac{2\left(k+2\right)}{k\left(k+2\right)}$$

Since \frac{5kk}{k\left(k+2\right)} and \frac{2\left(k+2\right)}{k\left(k+2\right)} have the same denominator, add them by adding their numerators.

$$\frac{5kk+2\left(k+2\right)}{k\left(k+2\right)}$$

Do the multiplications in 5kk+2\left(k+2\right).

$$\frac{5k^{2}+2k+4}{k\left(k+2\right)}$$

Expand k\left(k+2\right).

$$\frac{5k^{2}+2k+4}{k^{2}+2k}$$

Factor

$$\frac{5k^{2}+2k+4}{k\left(k+2\right)}$$