Solve x+2x/3+2/3*2x/3

$$x+ \frac{ 2x }{ 3 } + \frac{ 2 }{ 3 } \times \frac{ 2x }{ 3 }$$

Evaluate

$$\frac{19x}{9}$$

Short Solution Steps

Multiply \frac{2}{3} times \frac{2x}{3} by multiplying numerator times numerator and denominator times denominator.

$$x+\frac{2x}{3}+\frac{2\times 2x}{3\times 3}$$

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

$$\frac{3x}{3}+\frac{2x}{3}+\frac{2\times 2x}{3\times 3}$$

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

$$\frac{3x+2x}{3}+\frac{2\times 2x}{3\times 3}$$

Combine like terms in 3x+2x.

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

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

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

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

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

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

$$\frac{15x+4x}{3\times 3}$$

Combine like terms in 15x+4x.

$$\frac{19x}{3\times 3}$$

Expand 3\times 3.

$$\frac{19x}{9}$$

Differentiate w.r.t. x

$$\frac{19}{9} = 2\frac{1}{9} = 2.111111111111111$$