Solve 3m-9+2m-4-m+1/left(m-2right)left(m-1right)left(m-3right)

$$\frac{ 3m-9+2m-4-m+1 }{ \left( m-2 \right) \left( m-1 \right) \left( m-3 \right) }$$

Evaluate

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

Short Solution Steps

Combine 3m and 2m to get 5m.

$$\frac{5m-9-4-m+1}{\left(m-2\right)\left(m-1\right)\left(m-3\right)}$$

Subtract 4 from -9 to get -13.

$$\frac{5m-13-m+1}{\left(m-2\right)\left(m-1\right)\left(m-3\right)}$$

Combine 5m and -m to get 4m.

$$\frac{4m-13+1}{\left(m-2\right)\left(m-1\right)\left(m-3\right)}$$

Add -13 and 1 to get -12.

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

Factor the expressions that are not already factored.

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

Cancel out m-3 in both numerator and denominator.

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

Expand the expression.

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

Expand

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

Short Solution Steps

Combine 3m and 2m to get 5m.

$$\frac{5m-9-4-m+1}{\left(m-2\right)\left(m-1\right)\left(m-3\right)}$$

Subtract 4 from -9 to get -13.

$$\frac{5m-13-m+1}{\left(m-2\right)\left(m-1\right)\left(m-3\right)}$$

Combine 5m and -m to get 4m.

$$\frac{4m-13+1}{\left(m-2\right)\left(m-1\right)\left(m-3\right)}$$

Add -13 and 1 to get -12.

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

Factor the expressions that are not already factored.

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

Cancel out m-3 in both numerator and denominator.

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

Expand the expression.

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