Solve 5/3x-2-x/x^2-5x

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

Evaluate

$$\frac{8x-31}{3x\left(x-5\right)}$$

Short Solution Steps

Factor x^{2}-5x.

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

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

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

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

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

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

$$\frac{5x-25-6+3x}{3x\left(x-5\right)}$$

Combine like terms in 5x-25-6+3x.

$$\frac{8x-31}{3x\left(x-5\right)}$$

Expand 3x\left(x-5\right).

$$\frac{8x-31}{3x^{2}-15x}$$

Expand

$$\frac{8x-31}{3x\left(x-5\right)}$$

Short Solution Steps

Factor x^{2}-5x.

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

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

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

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

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

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

$$\frac{5x-25-6+3x}{3x\left(x-5\right)}$$

Combine like terms in 5x-25-6+3x.

$$\frac{8x-31}{3x\left(x-5\right)}$$

Expand 3x\left(x-5\right).

$$\frac{8x-31}{3x^{2}-15x}$$