Solve 8-8/w/8-frac{8{w-1}}

$$\frac { 8 - \frac { 8 } { w } } { 8 - \frac { 8 } { w - 1 } }$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 8 times \frac{w}{w}.

$$\frac{\frac{8w}{w}-\frac{8}{w}}{8-\frac{8}{w-1}}$$

Since \frac{8w}{w} and \frac{8}{w} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{8w-8}{w}}{8-\frac{8}{w-1}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 8 times \frac{w-1}{w-1}.

$$\frac{\frac{8w-8}{w}}{\frac{8\left(w-1\right)}{w-1}-\frac{8}{w-1}}$$

Since \frac{8\left(w-1\right)}{w-1} and \frac{8}{w-1} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{8w-8}{w}}{\frac{8\left(w-1\right)-8}{w-1}}$$

Do the multiplications in 8\left(w-1\right)-8.

$$\frac{\frac{8w-8}{w}}{\frac{8w-8-8}{w-1}}$$

Combine like terms in 8w-8-8.

$$\frac{\frac{8w-8}{w}}{\frac{8w-16}{w-1}}$$

Divide \frac{8w-8}{w} by \frac{8w-16}{w-1} by multiplying \frac{8w-8}{w} by the reciprocal of \frac{8w-16}{w-1}.

$$\frac{\left(8w-8\right)\left(w-1\right)}{w\left(8w-16\right)}$$

Factor the expressions that are not already factored.

$$\frac{8\left(w-1\right)^{2}}{8w\left(w-2\right)}$$

Cancel out 8 in both numerator and denominator.

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

Expand the expression.

$$\frac{w^{2}-2w+1}{w^{2}-2w}$$

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 8 times \frac{w}{w}.

$$\frac{\frac{8w}{w}-\frac{8}{w}}{8-\frac{8}{w-1}}$$

Since \frac{8w}{w} and \frac{8}{w} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{8w-8}{w}}{8-\frac{8}{w-1}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 8 times \frac{w-1}{w-1}.

$$\frac{\frac{8w-8}{w}}{\frac{8\left(w-1\right)}{w-1}-\frac{8}{w-1}}$$

Since \frac{8\left(w-1\right)}{w-1} and \frac{8}{w-1} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{8w-8}{w}}{\frac{8\left(w-1\right)-8}{w-1}}$$

Do the multiplications in 8\left(w-1\right)-8.

$$\frac{\frac{8w-8}{w}}{\frac{8w-8-8}{w-1}}$$

Combine like terms in 8w-8-8.

$$\frac{\frac{8w-8}{w}}{\frac{8w-16}{w-1}}$$

Divide \frac{8w-8}{w} by \frac{8w-16}{w-1} by multiplying \frac{8w-8}{w} by the reciprocal of \frac{8w-16}{w-1}.

$$\frac{\left(8w-8\right)\left(w-1\right)}{w\left(8w-16\right)}$$

Factor the expressions that are not already factored.

$$\frac{8\left(w-1\right)^{2}}{8w\left(w-2\right)}$$

Cancel out 8 in both numerator and denominator.

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

Expand the expression.

$$\frac{w^{2}-2w+1}{w^{2}-2w}$$