Solve left(x-1right)left(1+x-2+1/x-2-1+x+1-1/x-1--1left(1+x-2+1/x-2-1right)right)

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

Evaluate

$$\frac{4\left(x-2\right)\left(x-1\right)}{x-3}$$

Short Solution Steps

Add -2 and 1 to get -1.

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

Subtract 1 from -2 to get -3.

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

Subtract 1 from 1 to get 0.

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

The opposite of -1 is 1.

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

Add -1 and 1 to get 0.

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

Cancel out x in both numerator and denominator.

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

Add -2 and 1 to get -1.

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

Subtract 1 from -2 to get -3.

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

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

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

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

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

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

$$\left(x-1\right)\left(1+\frac{x-1}{x-3}+1\times \frac{2x-4}{x-3}\right)$$

Express 1\times \frac{2x-4}{x-3} as a single fraction.

$$\left(x-1\right)\left(1+\frac{x-1}{x-3}+\frac{2x-4}{x-3}\right)$$

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

$$\left(x-1\right)\left(\frac{x-3}{x-3}+\frac{x-1}{x-3}+\frac{2x-4}{x-3}\right)$$

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

$$\left(x-1\right)\left(\frac{x-3+x-1}{x-3}+\frac{2x-4}{x-3}\right)$$

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

$$\left(x-1\right)\left(\frac{2x-4}{x-3}+\frac{2x-4}{x-3}\right)$$

Since \frac{2x-4}{x-3} and \frac{2x-4}{x-3} have the same denominator, add them by adding their numerators.

$$\left(x-1\right)\times \frac{2x-4+2x-4}{x-3}$$

Combine like terms in 2x-4+2x-4.

$$\left(x-1\right)\times \frac{4x-8}{x-3}$$

Express \left(x-1\right)\times \frac{4x-8}{x-3} as a single fraction.

$$\frac{\left(x-1\right)\left(4x-8\right)}{x-3}$$

Apply the distributive property by multiplying each term of x-1 by each term of 4x-8.

$$\frac{4x^{2}-8x-4x+8}{x-3}$$

Combine -8x and -4x to get -12x.

$$\frac{4x^{2}-12x+8}{x-3}$$

Expand

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

Short Solution Steps

Add -2 and 1 to get -1.

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

Subtract 1 from -2 to get -3.

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

Subtract 1 from 1 to get 0.

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

The opposite of -1 is 1.

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

Add -1 and 1 to get 0.

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

Cancel out x in both numerator and denominator.

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

Add -2 and 1 to get -1.

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

Subtract 1 from -2 to get -3.

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

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

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

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

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

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

$$\left(x-1\right)\left(1+\frac{x-1}{x-3}+1\times \frac{2x-4}{x-3}\right)$$

Express 1\times \frac{2x-4}{x-3} as a single fraction.

$$\left(x-1\right)\left(1+\frac{x-1}{x-3}+\frac{2x-4}{x-3}\right)$$

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

$$\left(x-1\right)\left(\frac{x-3}{x-3}+\frac{x-1}{x-3}+\frac{2x-4}{x-3}\right)$$

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

$$\left(x-1\right)\left(\frac{x-3+x-1}{x-3}+\frac{2x-4}{x-3}\right)$$

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

$$\left(x-1\right)\left(\frac{2x-4}{x-3}+\frac{2x-4}{x-3}\right)$$

Since \frac{2x-4}{x-3} and \frac{2x-4}{x-3} have the same denominator, add them by adding their numerators.

$$\left(x-1\right)\times \frac{2x-4+2x-4}{x-3}$$

Combine like terms in 2x-4+2x-4.

$$\left(x-1\right)\times \frac{4x-8}{x-3}$$

Express \left(x-1\right)\times \frac{4x-8}{x-3} as a single fraction.

$$\frac{\left(x-1\right)\left(4x-8\right)}{x-3}$$

Apply the distributive property by multiplying each term of x-1 by each term of 4x-8.

$$\frac{4x^{2}-8x-4x+8}{x-3}$$

Combine -8x and -4x to get -12x.

$$\frac{4x^{2}-12x+8}{x-3}$$