Solve -1-x-1/3x-2/x-1

$$- \frac{ 1- \frac{ x-1 }{ 3x-2 } }{ x-1 }$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{3x-2}{3x-2}.

$$-\frac{\frac{3x-2}{3x-2}-\frac{x-1}{3x-2}}{x-1}$$

Since \frac{3x-2}{3x-2} and \frac{x-1}{3x-2} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 3x-2-\left(x-1\right).

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

Combine like terms in 3x-2-x+1.

$$-\frac{\frac{2x-1}{3x-2}}{x-1}$$

Express \frac{\frac{2x-1}{3x-2}}{x-1} as a single fraction.

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

Apply the distributive property by multiplying each term of 3x-2 by each term of x-1.

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

Combine -3x and -2x to get -5x.

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

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{3x-2}{3x-2}.

$$-\frac{\frac{3x-2}{3x-2}-\frac{x-1}{3x-2}}{x-1}$$

Since \frac{3x-2}{3x-2} and \frac{x-1}{3x-2} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 3x-2-\left(x-1\right).

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

Combine like terms in 3x-2-x+1.

$$-\frac{\frac{2x-1}{3x-2}}{x-1}$$

Express \frac{\frac{2x-1}{3x-2}}{x-1} as a single fraction.

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

Apply the distributive property by multiplying each term of 3x-2 by each term of x-1.

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

Combine -3x and -2x to get -5x.

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