Solve 4-x/x^2-x-1

$$\frac { 4 - x } { x ^ { 2 } - x } - 1$$

Evaluate

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

Short Solution Steps

Factor x^{2}-x.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x\left(x-1\right)}{x\left(x-1\right)}.

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

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

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

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

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

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

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

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

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

Expand

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

Short Solution Steps

Factor x^{2}-x.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x\left(x-1\right)}{x\left(x-1\right)}.

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

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

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

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

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

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

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

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

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