Solve m^2-4m+4/m-1div(3/m-1-m-1)

$$\frac { m ^ { 2 } - 4 m + 4 } { m - 1 } \div ( \frac { 3 } { m - 1 } - m - 1 )$$

Evaluate

$$-\frac{m-2}{m+2}$$

Short Solution Steps

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

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

Since \frac{3}{m-1} and \frac{\left(-m-1\right)\left(m-1\right)}{m-1} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 3+\left(-m-1\right)\left(m-1\right).

$$\frac{\frac{m^{2}-4m+4}{m-1}}{\frac{3-m^{2}+m-m+1}{m-1}}$$

Combine like terms in 3-m^{2}+m-m+1.

$$\frac{\frac{m^{2}-4m+4}{m-1}}{\frac{4-m^{2}}{m-1}}$$

Divide \frac{m^{2}-4m+4}{m-1} by \frac{4-m^{2}}{m-1} by multiplying \frac{m^{2}-4m+4}{m-1} by the reciprocal of \frac{4-m^{2}}{m-1}.

$$\frac{\left(m^{2}-4m+4\right)\left(m-1\right)}{\left(m-1\right)\left(4-m^{2}\right)}$$

Cancel out m-1 in both numerator and denominator.

$$\frac{m^{2}-4m+4}{-m^{2}+4}$$

Factor the expressions that are not already factored.

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

Cancel out m-2 in both numerator and denominator.

$$\frac{m-2}{-m-2}$$

Expand

$$-\frac{m-2}{m+2}$$

Short Solution Steps

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

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

Since \frac{3}{m-1} and \frac{\left(-m-1\right)\left(m-1\right)}{m-1} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 3+\left(-m-1\right)\left(m-1\right).

$$\frac{\frac{m^{2}-4m+4}{m-1}}{\frac{3-m^{2}+m-m+1}{m-1}}$$

Combine like terms in 3-m^{2}+m-m+1.

$$\frac{\frac{m^{2}-4m+4}{m-1}}{\frac{4-m^{2}}{m-1}}$$

Divide \frac{m^{2}-4m+4}{m-1} by \frac{4-m^{2}}{m-1} by multiplying \frac{m^{2}-4m+4}{m-1} by the reciprocal of \frac{4-m^{2}}{m-1}.

$$\frac{\left(m^{2}-4m+4\right)\left(m-1\right)}{\left(m-1\right)\left(4-m^{2}\right)}$$

Cancel out m-1 in both numerator and denominator.

$$\frac{m^{2}-4m+4}{-m^{2}+4}$$

Factor the expressions that are not already factored.

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

Cancel out m-2 in both numerator and denominator.

$$\frac{m-2}{-m-2}$$