Solve 5m+10/m^2-2m-3+4/m-3

$$\frac { 5 m + 10 } { m ^ { 2 } - 2 m - 3 } + \frac { 4 } { m - 3 }$$

Evaluate

$$\frac{9m+14}{\left(m-3\right)\left(m+1\right)}$$

Short Solution Steps

Factor m^{2}-2m-3.

$$\frac{5m+10}{\left(m-3\right)\left(m+1\right)}+\frac{4}{m-3}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(m-3\right)\left(m+1\right) and m-3 is \left(m-3\right)\left(m+1\right). Multiply \frac{4}{m-3} times \frac{m+1}{m+1}.

$$\frac{5m+10}{\left(m-3\right)\left(m+1\right)}+\frac{4\left(m+1\right)}{\left(m-3\right)\left(m+1\right)}$$

Since \frac{5m+10}{\left(m-3\right)\left(m+1\right)} and \frac{4\left(m+1\right)}{\left(m-3\right)\left(m+1\right)} have the same denominator, add them by adding their numerators.

$$\frac{5m+10+4\left(m+1\right)}{\left(m-3\right)\left(m+1\right)}$$

Do the multiplications in 5m+10+4\left(m+1\right).

$$\frac{5m+10+4m+4}{\left(m-3\right)\left(m+1\right)}$$

Combine like terms in 5m+10+4m+4.

$$\frac{9m+14}{\left(m-3\right)\left(m+1\right)}$$

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

$$\frac{9m+14}{m^{2}-2m-3}$$

Expand

$$\frac{9m+14}{\left(m-3\right)\left(m+1\right)}$$

Short Solution Steps

Factor m^{2}-2m-3.

$$\frac{5m+10}{\left(m-3\right)\left(m+1\right)}+\frac{4}{m-3}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(m-3\right)\left(m+1\right) and m-3 is \left(m-3\right)\left(m+1\right). Multiply \frac{4}{m-3} times \frac{m+1}{m+1}.

$$\frac{5m+10}{\left(m-3\right)\left(m+1\right)}+\frac{4\left(m+1\right)}{\left(m-3\right)\left(m+1\right)}$$

Since \frac{5m+10}{\left(m-3\right)\left(m+1\right)} and \frac{4\left(m+1\right)}{\left(m-3\right)\left(m+1\right)} have the same denominator, add them by adding their numerators.

$$\frac{5m+10+4\left(m+1\right)}{\left(m-3\right)\left(m+1\right)}$$

Do the multiplications in 5m+10+4\left(m+1\right).

$$\frac{5m+10+4m+4}{\left(m-3\right)\left(m+1\right)}$$

Combine like terms in 5m+10+4m+4.

$$\frac{9m+14}{\left(m-3\right)\left(m+1\right)}$$

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

$$\frac{9m+14}{m^{2}-2m-3}$$