Solve 5a/b-3a/2b+9/3b

$$\frac { 5 a } { b } - \frac { 3 a } { 2 b } + \frac { 9 } { 3 b }$$

Evaluate

$$\frac{7a+6}{2b}$$

Short Solution Steps

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

$$\frac{2\times 5a}{2b}-\frac{3a}{2b}+\frac{9}{3b}$$

Since \frac{2\times 5a}{2b} and \frac{3a}{2b} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\times 5a-3a}{2b}+\frac{9}{3b}$$

Do the multiplications in 2\times 5a-3a.

$$\frac{10a-3a}{2b}+\frac{9}{3b}$$

Combine like terms in 10a-3a.

$$\frac{7a}{2b}+\frac{9}{3b}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2b and 3b is 6b. Multiply \frac{7a}{2b} times \frac{3}{3}. Multiply \frac{9}{3b} times \frac{2}{2}.

$$\frac{3\times 7a}{6b}+\frac{9\times 2}{6b}$$

Since \frac{3\times 7a}{6b} and \frac{9\times 2}{6b} have the same denominator, add them by adding their numerators.

$$\frac{3\times 7a+9\times 2}{6b}$$

Do the multiplications in 3\times 7a+9\times 2.

$$\frac{21a+18}{6b}$$

Factor the expressions that are not already factored in \frac{21a+18}{6b}.

$$\frac{3\left(7a+6\right)}{6b}$$

Cancel out 3 in both numerator and denominator.

$$\frac{7a+6}{2b}$$

Factor

$$\frac{7a+6}{2b}$$