Solve 4/2a+5a+2/3a+5/6=

$$\frac { 4 } { 2 a } + \frac { 5 a + 2 } { 3 a } + \frac { 5 } { 6 } =$$

Evaluate

$$\frac{5}{2}+\frac{8}{3a}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2a and 3a is 6a. Multiply \frac{4}{2a} times \frac{3}{3}. Multiply \frac{5a+2}{3a} times \frac{2}{2}.

$$\frac{4\times 3}{6a}+\frac{2\left(5a+2\right)}{6a}+\frac{5}{6}$$

Since \frac{4\times 3}{6a} and \frac{2\left(5a+2\right)}{6a} have the same denominator, add them by adding their numerators.

$$\frac{4\times 3+2\left(5a+2\right)}{6a}+\frac{5}{6}$$

Do the multiplications in 4\times 3+2\left(5a+2\right).

$$\frac{12+10a+4}{6a}+\frac{5}{6}$$

Combine like terms in 12+10a+4.

$$\frac{16+10a}{6a}+\frac{5}{6}$$

Factor the expressions that are not already factored in \frac{16+10a}{6a}.

$$\frac{2\left(5a+8\right)}{6a}+\frac{5}{6}$$

Cancel out 2 in both numerator and denominator.

$$\frac{5a+8}{3a}+\frac{5}{6}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3a and 6 is 6a. Multiply \frac{5a+8}{3a} times \frac{2}{2}. Multiply \frac{5}{6} times \frac{a}{a}.

$$\frac{2\left(5a+8\right)}{6a}+\frac{5a}{6a}$$

Since \frac{2\left(5a+8\right)}{6a} and \frac{5a}{6a} have the same denominator, add them by adding their numerators.

$$\frac{2\left(5a+8\right)+5a}{6a}$$

Do the multiplications in 2\left(5a+8\right)+5a.

$$\frac{10a+16+5a}{6a}$$

Combine like terms in 10a+16+5a.

$$\frac{15a+16}{6a}$$

Expand

$$\frac{5}{2}+\frac{8}{3a}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2a and 3a is 6a. Multiply \frac{4}{2a} times \frac{3}{3}. Multiply \frac{5a+2}{3a} times \frac{2}{2}.

$$\frac{4\times 3}{6a}+\frac{2\left(5a+2\right)}{6a}+\frac{5}{6}$$

Since \frac{4\times 3}{6a} and \frac{2\left(5a+2\right)}{6a} have the same denominator, add them by adding their numerators.

$$\frac{4\times 3+2\left(5a+2\right)}{6a}+\frac{5}{6}$$

Do the multiplications in 4\times 3+2\left(5a+2\right).

$$\frac{12+10a+4}{6a}+\frac{5}{6}$$

Combine like terms in 12+10a+4.

$$\frac{16+10a}{6a}+\frac{5}{6}$$

Factor the expressions that are not already factored in \frac{16+10a}{6a}.

$$\frac{2\left(5a+8\right)}{6a}+\frac{5}{6}$$

Cancel out 2 in both numerator and denominator.

$$\frac{5a+8}{3a}+\frac{5}{6}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3a and 6 is 6a. Multiply \frac{5a+8}{3a} times \frac{2}{2}. Multiply \frac{5}{6} times \frac{a}{a}.

$$\frac{2\left(5a+8\right)}{6a}+\frac{5a}{6a}$$

Since \frac{2\left(5a+8\right)}{6a} and \frac{5a}{6a} have the same denominator, add them by adding their numerators.

$$\frac{2\left(5a+8\right)+5a}{6a}$$

Do the multiplications in 2\left(5a+8\right)+5a.

$$\frac{10a+16+5a}{6a}$$

Combine like terms in 10a+16+5a.

$$\frac{15a+16}{6a}$$