Solve 2(x-1)/x-4-x+6/x

$$\frac{ 2(x-1) }{ x-4 } - \frac{ x+6 }{ x }$$

Evaluate

$$\frac{x^{2}-4x+24}{x\left(x-4\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-4 and x is x\left(x-4\right). Multiply \frac{2\left(x-1\right)}{x-4} times \frac{x}{x}. Multiply \frac{x+6}{x} times \frac{x-4}{x-4}.

$$\frac{2\left(x-1\right)x}{x\left(x-4\right)}-\frac{\left(x+6\right)\left(x-4\right)}{x\left(x-4\right)}$$

Since \frac{2\left(x-1\right)x}{x\left(x-4\right)} and \frac{\left(x+6\right)\left(x-4\right)}{x\left(x-4\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\left(x-1\right)x-\left(x+6\right)\left(x-4\right)}{x\left(x-4\right)}$$

Do the multiplications in 2\left(x-1\right)x-\left(x+6\right)\left(x-4\right).

$$\frac{2x^{2}-2x-x^{2}+4x-6x+24}{x\left(x-4\right)}$$

Combine like terms in 2x^{2}-2x-x^{2}+4x-6x+24.

$$\frac{x^{2}-4x+24}{x\left(x-4\right)}$$

Expand x\left(x-4\right).

$$\frac{x^{2}-4x+24}{x^{2}-4x}$$

Expand

$$\frac{x^{2}-4x+24}{x\left(x-4\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-4 and x is x\left(x-4\right). Multiply \frac{2\left(x-1\right)}{x-4} times \frac{x}{x}. Multiply \frac{x+6}{x} times \frac{x-4}{x-4}.

$$\frac{2\left(x-1\right)x}{x\left(x-4\right)}-\frac{\left(x+6\right)\left(x-4\right)}{x\left(x-4\right)}$$

Since \frac{2\left(x-1\right)x}{x\left(x-4\right)} and \frac{\left(x+6\right)\left(x-4\right)}{x\left(x-4\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\left(x-1\right)x-\left(x+6\right)\left(x-4\right)}{x\left(x-4\right)}$$

Do the multiplications in 2\left(x-1\right)x-\left(x+6\right)\left(x-4\right).

$$\frac{2x^{2}-2x-x^{2}+4x-6x+24}{x\left(x-4\right)}$$

Combine like terms in 2x^{2}-2x-x^{2}+4x-6x+24.

$$\frac{x^{2}-4x+24}{x\left(x-4\right)}$$

Expand x\left(x-4\right).

$$\frac{x^{2}-4x+24}{x^{2}-4x}$$