Solve m^2-4m+3/m^2-1+m^2+6m/3m^2+21m+18

$$\frac { m ^ { 2 } - 4 m + 3 } { m ^ { 2 } - 1 } + \frac { m ^ { 2 } + 6 m } { 3 m ^ { 2 } + 21 m + 18 }$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{m^{2}-4m+3}{m^{2}-1}.

$$\frac{\left(m-3\right)\left(m-1\right)}{\left(m-1\right)\left(m+1\right)}+\frac{m^{2}+6m}{3m^{2}+21m+18}$$

Cancel out m-1 in both numerator and denominator.

$$\frac{m-3}{m+1}+\frac{m^{2}+6m}{3m^{2}+21m+18}$$

Factor the expressions that are not already factored in \frac{m^{2}+6m}{3m^{2}+21m+18}.

$$\frac{m-3}{m+1}+\frac{m\left(m+6\right)}{3\left(m+1\right)\left(m+6\right)}$$

Cancel out m+6 in both numerator and denominator.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of m+1 and 3\left(m+1\right) is 3\left(m+1\right). Multiply \frac{m-3}{m+1} times \frac{3}{3}.

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

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

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

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

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

Combine like terms in 3m-9+m.

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

Expand 3\left(m+1\right).

$$\frac{4m-9}{3m+3}$$

Expand

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{m^{2}-4m+3}{m^{2}-1}.

$$\frac{\left(m-3\right)\left(m-1\right)}{\left(m-1\right)\left(m+1\right)}+\frac{m^{2}+6m}{3m^{2}+21m+18}$$

Cancel out m-1 in both numerator and denominator.

$$\frac{m-3}{m+1}+\frac{m^{2}+6m}{3m^{2}+21m+18}$$

Factor the expressions that are not already factored in \frac{m^{2}+6m}{3m^{2}+21m+18}.

$$\frac{m-3}{m+1}+\frac{m\left(m+6\right)}{3\left(m+1\right)\left(m+6\right)}$$

Cancel out m+6 in both numerator and denominator.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of m+1 and 3\left(m+1\right) is 3\left(m+1\right). Multiply \frac{m-3}{m+1} times \frac{3}{3}.

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

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

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

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

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

Combine like terms in 3m-9+m.

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

Expand 3\left(m+1\right).

$$\frac{4m-9}{3m+3}$$