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

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

Evaluate

$$\frac{13a}{3b}$$

Short Solution Steps

Cancel out 3 in both numerator and denominator.

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

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

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

Combine like terms in 5a-a.

$$\frac{4a}{b}+\frac{a}{3b}$$

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

$$\frac{3\times 4a}{3b}+\frac{a}{3b}$$

Since \frac{3\times 4a}{3b} and \frac{a}{3b} have the same denominator, add them by adding their numerators.

$$\frac{3\times 4a+a}{3b}$$

Do the multiplications in 3\times 4a+a.

$$\frac{12a+a}{3b}$$

Combine like terms in 12a+a.

$$\frac{13a}{3b}$$

Differentiate w.r.t. a

$$\frac{13}{3b}$$