Solve 5a/6-4a/5=

$$\frac { 5 a } { 6 } - \frac { 4 a } { 5 } =$$

Evaluate

$$\frac{a}{30}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6 and 5 is 30. Multiply \frac{5a}{6} times \frac{5}{5}. Multiply \frac{4a}{5} times \frac{6}{6}.

$$\frac{5\times 5a}{30}-\frac{6\times 4a}{30}$$

Since \frac{5\times 5a}{30} and \frac{6\times 4a}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5\times 5a-6\times 4a}{30}$$

Do the multiplications in 5\times 5a-6\times 4a.

$$\frac{25a-24a}{30}$$

Combine like terms in 25a-24a.

$$\frac{a}{30}$$

Differentiate w.r.t. a

$$\frac{1}{30} = 0.03333333333333333$$

Steps Using Definition of a Derivative

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6 and 5 is 30. Multiply \frac{5a}{6} times \frac{5}{5}. Multiply \frac{4a}{5} times \frac{6}{6}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{5\times 5a}{30}-\frac{6\times 4a}{30})$$

Since \frac{5\times 5a}{30} and \frac{6\times 4a}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{5\times 5a-6\times 4a}{30})$$

Do the multiplications in 5\times 5a-6\times 4a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{25a-24a}{30})$$

Combine like terms in 25a-24a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a}{30})$$

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

$$\frac{1}{30}a^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{30}a^{0}$$

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

$$\frac{1}{30}\times 1$$

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

$$\frac{1}{30}$$