Solve (1-1/p)(1-1/p-1)(1-2/p-2)

$$( 1 - \frac { 1 } { p } ) ( 1 - \frac { 1 } { p - 1 } ) ( 1 - \frac { 2 } { p - 2 } )$$

Evaluate

$$\frac{p-4}{p}$$

Short Solution Steps

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

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

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

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

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

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

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

$$\frac{p-1}{p}\times \frac{p-1-1}{p-1}\left(1-\frac{2}{p-2}\right)$$

Combine like terms in p-1-1.

$$\frac{p-1}{p}\times \frac{p-2}{p-1}\left(1-\frac{2}{p-2}\right)$$

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

$$\frac{p-1}{p}\times \frac{p-2}{p-1}\left(\frac{p-2}{p-2}-\frac{2}{p-2}\right)$$

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

$$\frac{p-1}{p}\times \frac{p-2}{p-1}\times \frac{p-2-2}{p-2}$$

Combine like terms in p-2-2.

$$\frac{p-1}{p}\times \frac{p-2}{p-1}\times \frac{p-4}{p-2}$$

Multiply \frac{p-1}{p} times \frac{p-2}{p-1} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(p-1\right)\left(p-2\right)}{p\left(p-1\right)}\times \frac{p-4}{p-2}$$

Cancel out p-1 in both numerator and denominator.

$$\frac{p-2}{p}\times \frac{p-4}{p-2}$$

Multiply \frac{p-2}{p} times \frac{p-4}{p-2} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out p-2 in both numerator and denominator.

$$\frac{p-4}{p}$$

Expand

$$\frac{p-4}{p}$$

Short Solution Steps

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

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

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

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

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

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

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

$$\frac{p-1}{p}\times \frac{p-1-1}{p-1}\left(1-\frac{2}{p-2}\right)$$

Combine like terms in p-1-1.

$$\frac{p-1}{p}\times \frac{p-2}{p-1}\left(1-\frac{2}{p-2}\right)$$

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

$$\frac{p-1}{p}\times \frac{p-2}{p-1}\left(\frac{p-2}{p-2}-\frac{2}{p-2}\right)$$

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

$$\frac{p-1}{p}\times \frac{p-2}{p-1}\times \frac{p-2-2}{p-2}$$

Combine like terms in p-2-2.

$$\frac{p-1}{p}\times \frac{p-2}{p-1}\times \frac{p-4}{p-2}$$

Multiply \frac{p-1}{p} times \frac{p-2}{p-1} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(p-1\right)\left(p-2\right)}{p\left(p-1\right)}\times \frac{p-4}{p-2}$$

Cancel out p-1 in both numerator and denominator.

$$\frac{p-2}{p}\times \frac{p-4}{p-2}$$

Multiply \frac{p-2}{p} times \frac{p-4}{p-2} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out p-2 in both numerator and denominator.

$$\frac{p-4}{p}$$