Solve 3x/2-5x/3+x/4

$$\frac { 3 x } { 2 } - \frac { 5 x } { 3 } + \frac { x } { 4 }$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 3 is 6. Multiply \frac{3x}{2} times \frac{3}{3}. Multiply \frac{5x}{3} times \frac{2}{2}.

$$\frac{3\times 3x}{6}-\frac{2\times 5x}{6}+\frac{x}{4}$$

Since \frac{3\times 3x}{6} and \frac{2\times 5x}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\times 3x-2\times 5x}{6}+\frac{x}{4}$$

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

$$\frac{9x-10x}{6}+\frac{x}{4}$$

Combine like terms in 9x-10x.

$$\frac{-x}{6}+\frac{x}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6 and 4 is 12. Multiply \frac{-x}{6} times \frac{2}{2}. Multiply \frac{x}{4} times \frac{3}{3}.

$$\frac{2\left(-1\right)x}{12}+\frac{3x}{12}$$

Since \frac{2\left(-1\right)x}{12} and \frac{3x}{12} have the same denominator, add them by adding their numerators.

$$\frac{2\left(-1\right)x+3x}{12}$$

Do the multiplications in 2\left(-1\right)x+3x.

$$\frac{-2x+3x}{12}$$

Combine like terms in -2x+3x.

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

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 2 and 3 is 6. Multiply \frac{3x}{2} times \frac{3}{3}. Multiply \frac{5x}{3} times \frac{2}{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3\times 3x}{6}-\frac{2\times 5x}{6}+\frac{x}{4})$$

Since \frac{3\times 3x}{6} and \frac{2\times 5x}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3\times 3x-2\times 5x}{6}+\frac{x}{4})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{9x-10x}{6}+\frac{x}{4})$$

Combine like terms in 9x-10x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-x}{6}+\frac{x}{4})$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6 and 4 is 12. Multiply \frac{-x}{6} times \frac{2}{2}. Multiply \frac{x}{4} times \frac{3}{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2\left(-1\right)x}{12}+\frac{3x}{12})$$

Since \frac{2\left(-1\right)x}{12} and \frac{3x}{12} have the same denominator, add them by adding their numerators.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2\left(-1\right)x+3x}{12})$$

Do the multiplications in 2\left(-1\right)x+3x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-2x+3x}{12})$$

Combine like terms in -2x+3x.

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

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.

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