Solve 5y/2+y/6-2y/3=

$$\frac { 5 y } { 2 } + \frac { y } { 6 } - \frac { 2 y } { 3 } =$$

Evaluate

$$2y$$

Short Solution Steps

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

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

Since \frac{3\times 5y}{6} and \frac{y}{6} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 3\times 5y+y.

$$\frac{15y+y}{6}-\frac{2y}{3}$$

Combine like terms in 15y+y.

$$\frac{16y}{6}-\frac{2y}{3}$$

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

$$\frac{16y}{6}-\frac{2\times 2y}{6}$$

Since \frac{16y}{6} and \frac{2\times 2y}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{16y-2\times 2y}{6}$$

Do the multiplications in 16y-2\times 2y.

$$\frac{16y-4y}{6}$$

Combine like terms in 16y-4y.

$$\frac{12y}{6}$$

Divide 12y by 6 to get 2y.

$$2y$$

Differentiate w.r.t. y

$$2$$

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

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

Since \frac{3\times 5y}{6} and \frac{y}{6} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 3\times 5y+y.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{15y+y}{6}-\frac{2y}{3})$$

Combine like terms in 15y+y.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{16y}{6}-\frac{2y}{3})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{16y}{6}-\frac{2\times 2y}{6})$$

Since \frac{16y}{6} and \frac{2\times 2y}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{16y-2\times 2y}{6})$$

Do the multiplications in 16y-2\times 2y.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{16y-4y}{6})$$

Combine like terms in 16y-4y.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{12y}{6})$$

Divide 12y by 6 to get 2y.

$$\frac{\mathrm{d}}{\mathrm{d}y}(2y)$$

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

$$2y^{1-1}$$

Subtract 1 from 1.

$$2y^{0}$$

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

$$2\times 1$$

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

$$2$$