Solve (1-2/x-1)divx^2-x+6/x-1

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

Evaluate

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

Short Solution Steps

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

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

Since \frac{x-1}{x-1} and \frac{2}{x-1} have the same denominator, subtract them by subtracting their numerators.

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

Combine like terms in x-1-2.

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

Divide \frac{x-3}{x-1} by \frac{x^{2}-x+6}{x-1} by multiplying \frac{x-3}{x-1} by the reciprocal of \frac{x^{2}-x+6}{x-1}.

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

Cancel out x-1 in both numerator and denominator.

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

Expand

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

Short Solution Steps

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

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

Since \frac{x-1}{x-1} and \frac{2}{x-1} have the same denominator, subtract them by subtracting their numerators.

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

Combine like terms in x-1-2.

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

Divide \frac{x-3}{x-1} by \frac{x^{2}-x+6}{x-1} by multiplying \frac{x-3}{x-1} by the reciprocal of \frac{x^{2}-x+6}{x-1}.

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

Cancel out x-1 in both numerator and denominator.

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