Solve 2a/3+3a/2-5a/6

$$\frac { 2 a } { 3 } + \frac { 3 a } { 2 } - \frac { 5 a } { 6 }$$

Evaluate

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

Short Solution Steps

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

$$\frac{2\times 2a}{6}+\frac{3\times 3a}{6}-\frac{5a}{6}$$

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

$$\frac{2\times 2a+3\times 3a}{6}-\frac{5a}{6}$$

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

$$\frac{4a+9a}{6}-\frac{5a}{6}$$

Combine like terms in 4a+9a.

$$\frac{13a}{6}-\frac{5a}{6}$$

Since \frac{13a}{6} and \frac{5a}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{13a-5a}{6}$$

Combine like terms in 13a-5a.

$$\frac{8a}{6}$$

Divide 8a by 6 to get \frac{4}{3}a.

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

Differentiate w.r.t. a

$$\frac{4}{3} = 1\frac{1}{3} = 1.3333333333333333$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{2\times 2a}{6}+\frac{3\times 3a}{6}-\frac{5a}{6})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{2\times 2a+3\times 3a}{6}-\frac{5a}{6})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{4a+9a}{6}-\frac{5a}{6})$$

Combine like terms in 4a+9a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{13a}{6}-\frac{5a}{6})$$

Since \frac{13a}{6} and \frac{5a}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{13a-5a}{6})$$

Combine like terms in 13a-5a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{8a}{6})$$

Divide 8a by 6 to get \frac{4}{3}a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{4}{3}a)$$

The derivative of ax^{n} is nax^{n-1}.

$$\frac{4}{3}a^{1-1}$$

Subtract 1 from 1.

$$\frac{4}{3}a^{0}$$

For any term t except 0, t^{0}=1.

$$\frac{4}{3}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$\frac{4}{3}$$