Solve x-3/x-4-1/x

$$\frac { x - 3 } { x - 4 } - \frac { 1 } { x }$$

Evaluate

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

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{x-3}{x-4} times \frac{x}{x}. Multiply \frac{1}{x} times \frac{x-4}{x-4}.

$$\frac{\left(x-3\right)x}{x\left(x-4\right)}-\frac{x-4}{x\left(x-4\right)}$$

Since \frac{\left(x-3\right)x}{x\left(x-4\right)} and \frac{x-4}{x\left(x-4\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(x-3\right)x-\left(x-4\right)}{x\left(x-4\right)}$$

Do the multiplications in \left(x-3\right)x-\left(x-4\right).

$$\frac{x^{2}-3x-x+4}{x\left(x-4\right)}$$

Combine like terms in x^{2}-3x-x+4.

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

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

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

Expand

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

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{x-3}{x-4} times \frac{x}{x}. Multiply \frac{1}{x} times \frac{x-4}{x-4}.

$$\frac{\left(x-3\right)x}{x\left(x-4\right)}-\frac{x-4}{x\left(x-4\right)}$$

Since \frac{\left(x-3\right)x}{x\left(x-4\right)} and \frac{x-4}{x\left(x-4\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(x-3\right)x-\left(x-4\right)}{x\left(x-4\right)}$$

Do the multiplications in \left(x-3\right)x-\left(x-4\right).

$$\frac{x^{2}-3x-x+4}{x\left(x-4\right)}$$

Combine like terms in x^{2}-3x-x+4.

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

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

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