Solve x(5/3-2/x)(6/4)

$$x ( \frac { 5 } { 3 } - \frac { 2 } { x } ) ( \frac { 6 } { 4 } )$$

Evaluate

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

Short Solution Steps

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

$$x\left(\frac{5x}{3x}-\frac{2\times 3}{3x}\right)\times \frac{6}{4}$$

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

$$x\times \frac{5x-2\times 3}{3x}\times \frac{6}{4}$$

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

$$x\times \frac{5x-6}{3x}\times \frac{6}{4}$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

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

Express x\times \frac{5x-6}{3x} as a single fraction.

$$\frac{x\left(5x-6\right)}{3x}\times \frac{3}{2}$$

Cancel out x in both numerator and denominator.

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

Multiply \frac{5x-6}{3} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(5x-6\right)\times 3}{3\times 2}$$

Cancel out 3 in both numerator and denominator.

$$\frac{5x-6}{2}$$

Expand

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

Short Solution Steps

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

$$x\left(\frac{5x}{3x}-\frac{2\times 3}{3x}\right)\times \frac{6}{4}$$

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

$$x\times \frac{5x-2\times 3}{3x}\times \frac{6}{4}$$

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

$$x\times \frac{5x-6}{3x}\times \frac{6}{4}$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

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

Express x\times \frac{5x-6}{3x} as a single fraction.

$$\frac{x\left(5x-6\right)}{3x}\times \frac{3}{2}$$

Cancel out x in both numerator and denominator.

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

Multiply \frac{5x-6}{3} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(5x-6\right)\times 3}{3\times 2}$$

Cancel out 3 in both numerator and denominator.

$$\frac{5x-6}{2}$$