Simplify (6m)/(m-3)+m/(m+1)

$\frac{6 m}{m - 3} + \frac{m}{m + 1}$

Step 1

To write $\frac{6 m}{m - 3}$ as a fraction with a common denominator, multiply by $\frac{m + 1}{m + 1}$ .

$\frac{6 m}{m - 3} \cdot \frac{m + 1}{m + 1} + \frac{m}{m + 1}$

Step 2

To write $\frac{m}{m + 1}$ as a fraction with a common denominator, multiply by $\frac{m - 3}{m - 3}$ .

$\frac{6 m}{m - 3} \cdot \frac{m + 1}{m + 1} + \frac{m}{m + 1} \cdot \frac{m - 3}{m - 3}$

Step 3

Write each expression with a common denominator of $(m - 3) (m + 1)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{6 m}{m - 3}$ by $\frac{m + 1}{m + 1}$ .

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

Multiply $\frac{m}{m + 1}$ by $\frac{m - 3}{m - 3}$ .

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

Reorder the factors of $(m - 3) (m + 1)$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

Factor $m$ out of $6 m (m + 1) + m (m - 3)$ .

Factor $m$ out of $6 m (m + 1)$ .

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

Factor $m$ out of $m (6 (m + 1)) + m (m - 3)$ .

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

Apply the distributive property.

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

Multiply $6$ by $1$ .

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

Add $6 m$ and $m$ .

$\frac{m (7 m + 6 - 3)}{(m + 1) (m - 3)}$

Subtract $3$ from $6$ .

$\frac{m (7 m + 3)}{(m + 1) (m - 3)}$