Solve 7x/20-4x/15=

$$\frac { 7 x } { 20 } - \frac { 4 x } { 15 } =$$

Evaluate

$$\frac{x}{12}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 20 and 15 is 60. Multiply \frac{7x}{20} times \frac{3}{3}. Multiply \frac{4x}{15} times \frac{4}{4}.

$$\frac{3\times 7x}{60}-\frac{4\times 4x}{60}$$

Since \frac{3\times 7x}{60} and \frac{4\times 4x}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\times 7x-4\times 4x}{60}$$

Do the multiplications in 3\times 7x-4\times 4x.

$$\frac{21x-16x}{60}$$

Combine like terms in 21x-16x.

$$\frac{5x}{60}$$

Divide 5x by 60 to get \frac{1}{12}x.

$$\frac{1}{12}x$$

Differentiate w.r.t. x

$$\frac{1}{12} = 0.08333333333333333$$

Steps Using Definition of a Derivative

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 20 and 15 is 60. Multiply \frac{7x}{20} times \frac{3}{3}. Multiply \frac{4x}{15} times \frac{4}{4}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3\times 7x}{60}-\frac{4\times 4x}{60})$$

Since \frac{3\times 7x}{60} and \frac{4\times 4x}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3\times 7x-4\times 4x}{60})$$

Do the multiplications in 3\times 7x-4\times 4x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{21x-16x}{60})$$

Combine like terms in 21x-16x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5x}{60})$$

Divide 5x by 60 to get \frac{1}{12}x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{12}x)$$

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

$$\frac{1}{12}x^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{12}x^{0}$$

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

$$\frac{1}{12}\times 1$$

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

$$\frac{1}{12}$$