Solve a+2*1/a^2+2a=

$$a + 2 \cdot \frac { 1 } { a ^ { 2 } + 2 a } =$$

Evaluate

$$\frac{a^{3}+2a^{2}+2}{a\left(a+2\right)}$$

Short Solution Steps

Express 2\times \frac{1}{a^{2}+2a} as a single fraction.

$$a+\frac{2}{a^{2}+2a}$$

Factor a^{2}+2a.

$$a+\frac{2}{a\left(a+2\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply a times \frac{a\left(a+2\right)}{a\left(a+2\right)}.

$$\frac{aa\left(a+2\right)}{a\left(a+2\right)}+\frac{2}{a\left(a+2\right)}$$

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

$$\frac{aa\left(a+2\right)+2}{a\left(a+2\right)}$$

Do the multiplications in aa\left(a+2\right)+2.

$$\frac{a^{3}+2a^{2}+2}{a\left(a+2\right)}$$

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

$$\frac{a^{3}+2a^{2}+2}{a^{2}+2a}$$

Differentiate w.r.t. a

$$\frac{a^{4}+4a^{3}+4a^{2}-4a-4}{\left(a\left(a+2\right)\right)^{2}}$$