Solve a^2+6/6/a+frac{6{a}}=

$$\frac { \frac { a ^ { 2 } + 6 } { 6 } } { a + \frac { 6 } { a } } =$$

Evaluate

$$\frac{a}{6}$$

Short Solution Steps

Express \frac{\frac{a^{2}+6}{6}}{a+\frac{6}{a}} as a single fraction.

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

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

$$\frac{a^{2}+6}{6\left(\frac{aa}{a}+\frac{6}{a}\right)}$$

Since \frac{aa}{a} and \frac{6}{a} have the same denominator, add them by adding their numerators.

$$\frac{a^{2}+6}{6\times \frac{aa+6}{a}}$$

Do the multiplications in aa+6.

$$\frac{a^{2}+6}{6\times \frac{a^{2}+6}{a}}$$

Express 6\times \frac{a^{2}+6}{a} as a single fraction.

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

Divide a^{2}+6 by \frac{6\left(a^{2}+6\right)}{a} by multiplying a^{2}+6 by the reciprocal of \frac{6\left(a^{2}+6\right)}{a}.

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

Cancel out a^{2}+6 in both numerator and denominator.

$$\frac{a}{6}$$

Expand

$$\frac{a}{6}$$

Short Solution Steps

Express \frac{\frac{a^{2}+6}{6}}{a+\frac{6}{a}} as a single fraction.

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

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

$$\frac{a^{2}+6}{6\left(\frac{aa}{a}+\frac{6}{a}\right)}$$

Since \frac{aa}{a} and \frac{6}{a} have the same denominator, add them by adding their numerators.

$$\frac{a^{2}+6}{6\times \frac{aa+6}{a}}$$

Do the multiplications in aa+6.

$$\frac{a^{2}+6}{6\times \frac{a^{2}+6}{a}}$$

Express 6\times \frac{a^{2}+6}{a} as a single fraction.

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

Divide a^{2}+6 by \frac{6\left(a^{2}+6\right)}{a} by multiplying a^{2}+6 by the reciprocal of \frac{6\left(a^{2}+6\right)}{a}.

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

Cancel out a^{2}+6 in both numerator and denominator.

$$\frac{a}{6}$$