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

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

Evaluate

$$\frac{13a}{2b}$$

Short Solution Steps

Cancel out 3 in both numerator and denominator.

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

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}.

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

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

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

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

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

Combine like terms in 10a-3a.

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

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

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

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

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

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

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

Combine like terms in 7a+6a.

$$\frac{13a}{2b}$$

Differentiate w.r.t. a

$$\frac{13}{2b}$$