Solve 2x/3+3x/4-x/6

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

Evaluate

$$\frac{5x}{4}$$

Short Solution Steps

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

$$\frac{4\times 2x}{12}+\frac{3\times 3x}{12}-\frac{x}{6}$$

Since \frac{4\times 2x}{12} and \frac{3\times 3x}{12} have the same denominator, add them by adding their numerators.

$$\frac{4\times 2x+3\times 3x}{12}-\frac{x}{6}$$

Do the multiplications in 4\times 2x+3\times 3x.

$$\frac{8x+9x}{12}-\frac{x}{6}$$

Combine like terms in 8x+9x.

$$\frac{17x}{12}-\frac{x}{6}$$

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

$$\frac{17x}{12}-\frac{2x}{12}$$

Since \frac{17x}{12} and \frac{2x}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{17x-2x}{12}$$

Combine like terms in 17x-2x.

$$\frac{15x}{12}$$

Divide 15x by 12 to get \frac{5}{4}x.

$$\frac{5}{4}x$$

Differentiate w.r.t. x

$$\frac{5}{4} = 1\frac{1}{4} = 1.25$$

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 4 is 12. Multiply \frac{2x}{3} times \frac{4}{4}. Multiply \frac{3x}{4} times \frac{3}{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4\times 2x}{12}+\frac{3\times 3x}{12}-\frac{x}{6})$$

Since \frac{4\times 2x}{12} and \frac{3\times 3x}{12} have the same denominator, add them by adding their numerators.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4\times 2x+3\times 3x}{12}-\frac{x}{6})$$

Do the multiplications in 4\times 2x+3\times 3x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{8x+9x}{12}-\frac{x}{6})$$

Combine like terms in 8x+9x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{17x}{12}-\frac{x}{6})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{17x}{12}-\frac{2x}{12})$$

Since \frac{17x}{12} and \frac{2x}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{17x-2x}{12})$$

Combine like terms in 17x-2x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{15x}{12})$$

Divide 15x by 12 to get \frac{5}{4}x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5}{4}x)$$

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

$$\frac{5}{4}x^{1-1}$$

Subtract 1 from 1.

$$\frac{5}{4}x^{0}$$

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

$$\frac{5}{4}\times 1$$

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

$$\frac{5}{4}$$