Solve m^2-6m+8/2m-2-10/m-4

$$\frac { m ^ { 2 } - 6 m + 8 } { 2 m - 2 } - \frac { 10 } { m - 4 }$$

Evaluate

$$\frac{m^{3}-10m^{2}+12m-12}{2\left(m-4\right)\left(m-1\right)}$$

Short Solution Steps

Factor 2m-2.

$$\frac{m^{2}-6m+8}{2\left(m-1\right)}-\frac{10}{m-4}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(m-1\right) and m-4 is 2\left(m-4\right)\left(m-1\right). Multiply \frac{m^{2}-6m+8}{2\left(m-1\right)} times \frac{m-4}{m-4}. Multiply \frac{10}{m-4} times \frac{2\left(m-1\right)}{2\left(m-1\right)}.

$$\frac{\left(m^{2}-6m+8\right)\left(m-4\right)}{2\left(m-4\right)\left(m-1\right)}-\frac{10\times 2\left(m-1\right)}{2\left(m-4\right)\left(m-1\right)}$$

Since \frac{\left(m^{2}-6m+8\right)\left(m-4\right)}{2\left(m-4\right)\left(m-1\right)} and \frac{10\times 2\left(m-1\right)}{2\left(m-4\right)\left(m-1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(m^{2}-6m+8\right)\left(m-4\right)-10\times 2\left(m-1\right)}{2\left(m-4\right)\left(m-1\right)}$$

Do the multiplications in \left(m^{2}-6m+8\right)\left(m-4\right)-10\times 2\left(m-1\right).

$$\frac{m^{3}-4m^{2}-6m^{2}+24m+8m-32-20m+20}{2\left(m-4\right)\left(m-1\right)}$$

Combine like terms in m^{3}-4m^{2}-6m^{2}+24m+8m-32-20m+20.

$$\frac{m^{3}-10m^{2}+12m-12}{2\left(m-4\right)\left(m-1\right)}$$

Expand 2\left(m-4\right)\left(m-1\right).

$$\frac{m^{3}-10m^{2}+12m-12}{2m^{2}-10m+8}$$

Expand

$$\frac{m^{3}-10m^{2}+12m-12}{2\left(m-4\right)\left(m-1\right)}$$

Short Solution Steps

Factor 2m-2.

$$\frac{m^{2}-6m+8}{2\left(m-1\right)}-\frac{10}{m-4}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(m-1\right) and m-4 is 2\left(m-4\right)\left(m-1\right). Multiply \frac{m^{2}-6m+8}{2\left(m-1\right)} times \frac{m-4}{m-4}. Multiply \frac{10}{m-4} times \frac{2\left(m-1\right)}{2\left(m-1\right)}.

$$\frac{\left(m^{2}-6m+8\right)\left(m-4\right)}{2\left(m-4\right)\left(m-1\right)}-\frac{10\times 2\left(m-1\right)}{2\left(m-4\right)\left(m-1\right)}$$

Since \frac{\left(m^{2}-6m+8\right)\left(m-4\right)}{2\left(m-4\right)\left(m-1\right)} and \frac{10\times 2\left(m-1\right)}{2\left(m-4\right)\left(m-1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(m^{2}-6m+8\right)\left(m-4\right)-10\times 2\left(m-1\right)}{2\left(m-4\right)\left(m-1\right)}$$

Do the multiplications in \left(m^{2}-6m+8\right)\left(m-4\right)-10\times 2\left(m-1\right).

$$\frac{m^{3}-4m^{2}-6m^{2}+24m+8m-32-20m+20}{2\left(m-4\right)\left(m-1\right)}$$

Combine like terms in m^{3}-4m^{2}-6m^{2}+24m+8m-32-20m+20.

$$\frac{m^{3}-10m^{2}+12m-12}{2\left(m-4\right)\left(m-1\right)}$$

Expand 2\left(m-4\right)\left(m-1\right).

$$\frac{m^{3}-10m^{2}+12m-12}{2m^{2}-10m+8}$$