Solve 2-2/u-8/1-frac{u-5{4u-32}}

$$\frac { 2 - \frac { 2 } { u - 8 } } { 1 - \frac { u - 5 } { 4 u - 32 } }$$

Evaluate

$$\frac{8}{3}\approx 2.666666667$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{u-8}{u-8}.

$$\frac{\frac{2\left(u-8\right)}{u-8}-\frac{2}{u-8}}{1-\frac{u-5}{4u-32}}$$

Since \frac{2\left(u-8\right)}{u-8} and \frac{2}{u-8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{2\left(u-8\right)-2}{u-8}}{1-\frac{u-5}{4u-32}}$$

Do the multiplications in 2\left(u-8\right)-2.

$$\frac{\frac{2u-16-2}{u-8}}{1-\frac{u-5}{4u-32}}$$

Combine like terms in 2u-16-2.

$$\frac{\frac{2u-18}{u-8}}{1-\frac{u-5}{4u-32}}$$

Factor 4u-32.

$$\frac{\frac{2u-18}{u-8}}{1-\frac{u-5}{4\left(u-8\right)}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{4\left(u-8\right)}{4\left(u-8\right)}.

$$\frac{\frac{2u-18}{u-8}}{\frac{4\left(u-8\right)}{4\left(u-8\right)}-\frac{u-5}{4\left(u-8\right)}}$$

Since \frac{4\left(u-8\right)}{4\left(u-8\right)} and \frac{u-5}{4\left(u-8\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{2u-18}{u-8}}{\frac{4\left(u-8\right)-\left(u-5\right)}{4\left(u-8\right)}}$$

Do the multiplications in 4\left(u-8\right)-\left(u-5\right).

$$\frac{\frac{2u-18}{u-8}}{\frac{4u-32-u+5}{4\left(u-8\right)}}$$

Combine like terms in 4u-32-u+5.

$$\frac{\frac{2u-18}{u-8}}{\frac{3u-27}{4\left(u-8\right)}}$$

Divide \frac{2u-18}{u-8} by \frac{3u-27}{4\left(u-8\right)} by multiplying \frac{2u-18}{u-8} by the reciprocal of \frac{3u-27}{4\left(u-8\right)}.

$$\frac{\left(2u-18\right)\times 4\left(u-8\right)}{\left(u-8\right)\left(3u-27\right)}$$

Cancel out u-8 in both numerator and denominator.

$$\frac{4\left(2u-18\right)}{3u-27}$$

Factor the expressions that are not already factored.

$$\frac{2\times 4\left(u-9\right)}{3\left(u-9\right)}$$

Cancel out u-9 in both numerator and denominator.

$$\frac{2\times 4}{3}$$

Multiply 2 and 4 to get 8.

$$\frac{8}{3}$$

Factor

$$\frac{2 ^ {3}}{3} = 2\frac{2}{3} = 2.6666666666666665$$