Solve 2/a+1/2a/a+frac{a{2}}

$$\frac { \frac { 2 } { a } + \frac { 1 } { 2 a } } { a + \frac { a } { 2 } }$$

Evaluate

$$\frac{5}{3a^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a and 2a is 2a. Multiply \frac{2}{a} times \frac{2}{2}.

$$\frac{\frac{2\times 2}{2a}+\frac{1}{2a}}{a+\frac{a}{2}}$$

Since \frac{2\times 2}{2a} and \frac{1}{2a} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2\times 2+1}{2a}}{a+\frac{a}{2}}$$

Do the multiplications in 2\times 2+1.

$$\frac{\frac{4+1}{2a}}{a+\frac{a}{2}}$$

Do the calculations in 4+1.

$$\frac{\frac{5}{2a}}{a+\frac{a}{2}}$$

Combine a and \frac{a}{2} to get \frac{3}{2}a.

$$\frac{\frac{5}{2a}}{\frac{3}{2}a}$$

Express \frac{\frac{5}{2a}}{\frac{3}{2}a} as a single fraction.

$$\frac{5}{2a\times \frac{3}{2}a}$$

Multiply a and a to get a^{2}.

$$\frac{5}{2a^{2}\times \frac{3}{2}}$$

Cancel out 2 and 2.

$$\frac{5}{3a^{2}}$$

Expand

$$\frac{5}{3a^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a and 2a is 2a. Multiply \frac{2}{a} times \frac{2}{2}.

$$\frac{\frac{2\times 2}{2a}+\frac{1}{2a}}{a+\frac{a}{2}}$$

Since \frac{2\times 2}{2a} and \frac{1}{2a} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2\times 2+1}{2a}}{a+\frac{a}{2}}$$

Do the multiplications in 2\times 2+1.

$$\frac{\frac{4+1}{2a}}{a+\frac{a}{2}}$$

Do the calculations in 4+1.

$$\frac{\frac{5}{2a}}{a+\frac{a}{2}}$$

Combine a and \frac{a}{2} to get \frac{3}{2}a.

$$\frac{\frac{5}{2a}}{\frac{3}{2}a}$$

Express \frac{\frac{5}{2a}}{\frac{3}{2}a} as a single fraction.

$$\frac{5}{2a\times \frac{3}{2}a}$$

Multiply a and a to get a^{2}.

$$\frac{5}{2a^{2}\times \frac{3}{2}}$$

Cancel out 2 and 2.

$$\frac{5}{3a^{2}}$$