Solve r^2-2r/r-2/r/1-frac{4{r}}

$$\frac { \frac { r ^ { 2 } - 2 r } { r } - \frac { 2 } { r } } { 1 - \frac { 4 } { r } }$$

Evaluate

$$\frac{r^{2}-2r-2}{r-4}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{r^{2}-2r}{r}.

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

Cancel out r in both numerator and denominator.

$$\frac{r-2-\frac{2}{r}}{1-\frac{4}{r}}$$

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

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

Since \frac{\left(r-2\right)r}{r} and \frac{2}{r} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in \left(r-2\right)r-2.

$$\frac{\frac{r^{2}-2r-2}{r}}{1-\frac{4}{r}}$$

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

$$\frac{\frac{r^{2}-2r-2}{r}}{\frac{r}{r}-\frac{4}{r}}$$

Since \frac{r}{r} and \frac{4}{r} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{r^{2}-2r-2}{r}}{\frac{r-4}{r}}$$

Divide \frac{r^{2}-2r-2}{r} by \frac{r-4}{r} by multiplying \frac{r^{2}-2r-2}{r} by the reciprocal of \frac{r-4}{r}.

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

Cancel out r in both numerator and denominator.

$$\frac{r^{2}-2r-2}{r-4}$$

Expand

$$\frac{r^{2}-2r-2}{r-4}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{r^{2}-2r}{r}.

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

Cancel out r in both numerator and denominator.

$$\frac{r-2-\frac{2}{r}}{1-\frac{4}{r}}$$

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

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

Since \frac{\left(r-2\right)r}{r} and \frac{2}{r} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in \left(r-2\right)r-2.

$$\frac{\frac{r^{2}-2r-2}{r}}{1-\frac{4}{r}}$$

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

$$\frac{\frac{r^{2}-2r-2}{r}}{\frac{r}{r}-\frac{4}{r}}$$

Since \frac{r}{r} and \frac{4}{r} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{r^{2}-2r-2}{r}}{\frac{r-4}{r}}$$

Divide \frac{r^{2}-2r-2}{r} by \frac{r-4}{r} by multiplying \frac{r^{2}-2r-2}{r} by the reciprocal of \frac{r-4}{r}.

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

Cancel out r in both numerator and denominator.

$$\frac{r^{2}-2r-2}{r-4}$$