Solve 4(4-m/m-2)^2-2m-4/m-2

$$4 ( \frac { 4 - m } { m - 2 } ) ^ { 2 } - 2 \frac { m - 4 } { m - 2 }$$

Evaluate

$$\frac{2\left(m-6\right)\left(m-4\right)}{\left(m-2\right)^{2}}$$

Short Solution Steps

To raise \frac{4-m}{m-2} to a power, raise both numerator and denominator to the power and then divide.

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

Express 4\times \frac{\left(4-m\right)^{2}}{\left(m-2\right)^{2}} as a single fraction.

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

Express 2\times \frac{m-4}{m-2} as a single fraction.

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

Use the distributive property to multiply 2 by m-4.

$$\frac{4\left(4-m\right)^{2}}{\left(m-2\right)^{2}}-\frac{2m-8}{m-2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(m-2\right)^{2} and m-2 is \left(m-2\right)^{2}. Multiply \frac{2m-8}{m-2} times \frac{m-2}{m-2}.

$$\frac{4\left(4-m\right)^{2}}{\left(m-2\right)^{2}}-\frac{\left(2m-8\right)\left(m-2\right)}{\left(m-2\right)^{2}}$$

Since \frac{4\left(4-m\right)^{2}}{\left(m-2\right)^{2}} and \frac{\left(2m-8\right)\left(m-2\right)}{\left(m-2\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4\left(4-m\right)^{2}-\left(2m-8\right)\left(m-2\right)}{\left(m-2\right)^{2}}$$

Do the multiplications in 4\left(4-m\right)^{2}-\left(2m-8\right)\left(m-2\right).

$$\frac{64-32m+4m^{2}-2m^{2}+4m+8m-16}{\left(m-2\right)^{2}}$$

Combine like terms in 64-32m+4m^{2}-2m^{2}+4m+8m-16.

$$\frac{48-20m+2m^{2}}{\left(m-2\right)^{2}}$$

Expand \left(m-2\right)^{2}.

$$\frac{48-20m+2m^{2}}{m^{2}-4m+4}$$

Expand

$$\frac{2\left(m^{2}-10m+24\right)}{\left(m-2\right)^{2}}$$

Short Solution Steps

To raise \frac{4-m}{m-2} to a power, raise both numerator and denominator to the power and then divide.

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

Express 4\times \frac{\left(4-m\right)^{2}}{\left(m-2\right)^{2}} as a single fraction.

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

Express 2\times \frac{m-4}{m-2} as a single fraction.

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

Use the distributive property to multiply 2 by m-4.

$$\frac{4\left(4-m\right)^{2}}{\left(m-2\right)^{2}}-\frac{2m-8}{m-2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(m-2\right)^{2} and m-2 is \left(m-2\right)^{2}. Multiply \frac{2m-8}{m-2} times \frac{m-2}{m-2}.

$$\frac{4\left(4-m\right)^{2}}{\left(m-2\right)^{2}}-\frac{\left(2m-8\right)\left(m-2\right)}{\left(m-2\right)^{2}}$$

Since \frac{4\left(4-m\right)^{2}}{\left(m-2\right)^{2}} and \frac{\left(2m-8\right)\left(m-2\right)}{\left(m-2\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4\left(4-m\right)^{2}-\left(2m-8\right)\left(m-2\right)}{\left(m-2\right)^{2}}$$

Do the multiplications in 4\left(4-m\right)^{2}-\left(2m-8\right)\left(m-2\right).

$$\frac{64-32m+4m^{2}-2m^{2}+4m+8m-16}{\left(m-2\right)^{2}}$$

Combine like terms in 64-32m+4m^{2}-2m^{2}+4m+8m-16.

$$\frac{48-20m+2m^{2}}{\left(m-2\right)^{2}}$$

Expand \left(m-2\right)^{2}.

$$\frac{48-20m+2m^{2}}{m^{2}-4m+4}$$