Solve 3/x-6/1-x-x+5/x^2-x

$$\frac { 3 } { x } - \frac { 6 } { 1 - x } - \frac { x + 5 } { x ^ { 2 } - x }$$

Evaluate

$$\frac{8}{x}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and 1-x is x\left(-x+1\right). Multiply \frac{3}{x} times \frac{-x+1}{-x+1}. Multiply \frac{6}{1-x} times \frac{x}{x}.

$$\frac{3\left(-x+1\right)}{x\left(-x+1\right)}-\frac{6x}{x\left(-x+1\right)}-\frac{x+5}{x^{2}-x}$$

Since \frac{3\left(-x+1\right)}{x\left(-x+1\right)} and \frac{6x}{x\left(-x+1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\left(-x+1\right)-6x}{x\left(-x+1\right)}-\frac{x+5}{x^{2}-x}$$

Do the multiplications in 3\left(-x+1\right)-6x.

$$\frac{-3x+3-6x}{x\left(-x+1\right)}-\frac{x+5}{x^{2}-x}$$

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

$$\frac{-9x+3}{x\left(-x+1\right)}-\frac{x+5}{x^{2}-x}$$

Factor x^{2}-x.

$$\frac{-9x+3}{x\left(-x+1\right)}-\frac{x+5}{x\left(x-1\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x\left(-x+1\right) and x\left(x-1\right) is x\left(x-1\right). Multiply \frac{-9x+3}{x\left(-x+1\right)} times \frac{-1}{-1}.

$$\frac{-\left(-9x+3\right)}{x\left(x-1\right)}-\frac{x+5}{x\left(x-1\right)}$$

Since \frac{-\left(-9x+3\right)}{x\left(x-1\right)} and \frac{x+5}{x\left(x-1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\left(-9x+3\right)-\left(x+5\right)}{x\left(x-1\right)}$$

Do the multiplications in -\left(-9x+3\right)-\left(x+5\right).

$$\frac{9x-3-x-5}{x\left(x-1\right)}$$

Combine like terms in 9x-3-x-5.

$$\frac{8x-8}{x\left(x-1\right)}$$

Factor the expressions that are not already factored in \frac{8x-8}{x\left(x-1\right)}.

$$\frac{8\left(x-1\right)}{x\left(x-1\right)}$$

Cancel out x-1 in both numerator and denominator.

$$\frac{8}{x}$$

Expand

$$\frac{8}{x}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and 1-x is x\left(-x+1\right). Multiply \frac{3}{x} times \frac{-x+1}{-x+1}. Multiply \frac{6}{1-x} times \frac{x}{x}.

$$\frac{3\left(-x+1\right)}{x\left(-x+1\right)}-\frac{6x}{x\left(-x+1\right)}-\frac{x+5}{x^{2}-x}$$

Since \frac{3\left(-x+1\right)}{x\left(-x+1\right)} and \frac{6x}{x\left(-x+1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\left(-x+1\right)-6x}{x\left(-x+1\right)}-\frac{x+5}{x^{2}-x}$$

Do the multiplications in 3\left(-x+1\right)-6x.

$$\frac{-3x+3-6x}{x\left(-x+1\right)}-\frac{x+5}{x^{2}-x}$$

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

$$\frac{-9x+3}{x\left(-x+1\right)}-\frac{x+5}{x^{2}-x}$$

Factor x^{2}-x.

$$\frac{-9x+3}{x\left(-x+1\right)}-\frac{x+5}{x\left(x-1\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x\left(-x+1\right) and x\left(x-1\right) is x\left(x-1\right). Multiply \frac{-9x+3}{x\left(-x+1\right)} times \frac{-1}{-1}.

$$\frac{-\left(-9x+3\right)}{x\left(x-1\right)}-\frac{x+5}{x\left(x-1\right)}$$

Since \frac{-\left(-9x+3\right)}{x\left(x-1\right)} and \frac{x+5}{x\left(x-1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\left(-9x+3\right)-\left(x+5\right)}{x\left(x-1\right)}$$

Do the multiplications in -\left(-9x+3\right)-\left(x+5\right).

$$\frac{9x-3-x-5}{x\left(x-1\right)}$$

Combine like terms in 9x-3-x-5.

$$\frac{8x-8}{x\left(x-1\right)}$$

Factor the expressions that are not already factored in \frac{8x-8}{x\left(x-1\right)}.

$$\frac{8\left(x-1\right)}{x\left(x-1\right)}$$

Cancel out x-1 in both numerator and denominator.

$$\frac{8}{x}$$