Solve 4x/2-5x/3=

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

Evaluate

$$\frac{x}{3}$$

Short Solution Steps

Divide 4x by 2 to get 2x.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 2x times \frac{3}{3}.

$$\frac{3\times 2x}{3}-\frac{5x}{3}$$

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

$$\frac{3\times 2x-5x}{3}$$

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

$$\frac{6x-5x}{3}$$

Combine like terms in 6x-5x.

$$\frac{x}{3}$$

Differentiate w.r.t. x

$$\frac{1}{3} = 0.3333333333333333$$

Steps Using Definition of a Derivative

Divide 4x by 2 to get 2x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x-\frac{5x}{3})$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2x times \frac{3}{3}.

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

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

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

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6x-5x}{3})$$

Combine like terms in 6x-5x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{3})$$

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

$$\frac{1}{3}x^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{3}x^{0}$$

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

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

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

$$\frac{1}{3}$$