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

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

Evaluate

$$\frac{23x}{6}$$

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{5x}{2} times \frac{3}{3}. Multiply \frac{2x}{3} times \frac{2}{2}.

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

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

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

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

$$\frac{15x-4x}{6}+2x$$

Combine like terms in 15x-4x.

$$\frac{11x}{6}+2x$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2x times \frac{6}{6}.

$$\frac{11x}{6}+\frac{6\times 2x}{6}$$

Since \frac{11x}{6} and \frac{6\times 2x}{6} have the same denominator, add them by adding their numerators.

$$\frac{11x+6\times 2x}{6}$$

Do the multiplications in 11x+6\times 2x.

$$\frac{11x+12x}{6}$$

Combine like terms in 11x+12x.

$$\frac{23x}{6}$$

Differentiate w.r.t. x

$$\frac{23}{6} = 3\frac{5}{6} = 3.8333333333333335$$