Solve 2x/x(x-1)-5/3x

$$\frac { 2 x } { x ( x - 1 ) } - \frac { 5 } { 3 x }$$

Evaluate

$$\frac{x+5}{3x\left(x-1\right)}$$

Short Solution Steps

Cancel out x in both numerator and denominator.

$$\frac{2}{x-1}-\frac{5}{3x}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-1 and 3x is 3x\left(x-1\right). Multiply \frac{2}{x-1} times \frac{3x}{3x}. Multiply \frac{5}{3x} times \frac{x-1}{x-1}.

$$\frac{2\times 3x}{3x\left(x-1\right)}-\frac{5\left(x-1\right)}{3x\left(x-1\right)}$$

Since \frac{2\times 3x}{3x\left(x-1\right)} and \frac{5\left(x-1\right)}{3x\left(x-1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\times 3x-5\left(x-1\right)}{3x\left(x-1\right)}$$

Do the multiplications in 2\times 3x-5\left(x-1\right).

$$\frac{6x-5x+5}{3x\left(x-1\right)}$$

Combine like terms in 6x-5x+5.

$$\frac{x+5}{3x\left(x-1\right)}$$

Expand 3x\left(x-1\right).

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

Expand

$$\frac{x+5}{3x\left(x-1\right)}$$

Short Solution Steps

Cancel out x in both numerator and denominator.

$$\frac{2}{x-1}-\frac{5}{3x}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-1 and 3x is 3x\left(x-1\right). Multiply \frac{2}{x-1} times \frac{3x}{3x}. Multiply \frac{5}{3x} times \frac{x-1}{x-1}.

$$\frac{2\times 3x}{3x\left(x-1\right)}-\frac{5\left(x-1\right)}{3x\left(x-1\right)}$$

Since \frac{2\times 3x}{3x\left(x-1\right)} and \frac{5\left(x-1\right)}{3x\left(x-1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\times 3x-5\left(x-1\right)}{3x\left(x-1\right)}$$

Do the multiplications in 2\times 3x-5\left(x-1\right).

$$\frac{6x-5x+5}{3x\left(x-1\right)}$$

Combine like terms in 6x-5x+5.

$$\frac{x+5}{3x\left(x-1\right)}$$

Expand 3x\left(x-1\right).

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