Solve (m-3-7/m+3)divm-4/2m+6

$$( m - 3 - \frac { 7 } { m + 3 } ) \div \frac { m - 4 } { 2 m + 6 }$$

Evaluate

$$2\left(m+4\right)$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply m-3 times \frac{m+3}{m+3}.

$$\frac{\frac{\left(m-3\right)\left(m+3\right)}{m+3}-\frac{7}{m+3}}{\frac{m-4}{2m+6}}$$

Since \frac{\left(m-3\right)\left(m+3\right)}{m+3} and \frac{7}{m+3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{\left(m-3\right)\left(m+3\right)-7}{m+3}}{\frac{m-4}{2m+6}}$$

Do the multiplications in \left(m-3\right)\left(m+3\right)-7.

$$\frac{\frac{m^{2}+3m-3m-9-7}{m+3}}{\frac{m-4}{2m+6}}$$

Combine like terms in m^{2}+3m-3m-9-7.

$$\frac{\frac{m^{2}-16}{m+3}}{\frac{m-4}{2m+6}}$$

Divide \frac{m^{2}-16}{m+3} by \frac{m-4}{2m+6} by multiplying \frac{m^{2}-16}{m+3} by the reciprocal of \frac{m-4}{2m+6}.

$$\frac{\left(m^{2}-16\right)\left(2m+6\right)}{\left(m+3\right)\left(m-4\right)}$$

Factor the expressions that are not already factored.

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

Cancel out \left(m-4\right)\left(m+3\right) in both numerator and denominator.

$$2\left(m+4\right)$$

Expand the expression.

$$2m+8$$

Expand

$$2m+8$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply m-3 times \frac{m+3}{m+3}.

$$\frac{\frac{\left(m-3\right)\left(m+3\right)}{m+3}-\frac{7}{m+3}}{\frac{m-4}{2m+6}}$$

Since \frac{\left(m-3\right)\left(m+3\right)}{m+3} and \frac{7}{m+3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{\left(m-3\right)\left(m+3\right)-7}{m+3}}{\frac{m-4}{2m+6}}$$

Do the multiplications in \left(m-3\right)\left(m+3\right)-7.

$$\frac{\frac{m^{2}+3m-3m-9-7}{m+3}}{\frac{m-4}{2m+6}}$$

Combine like terms in m^{2}+3m-3m-9-7.

$$\frac{\frac{m^{2}-16}{m+3}}{\frac{m-4}{2m+6}}$$

Divide \frac{m^{2}-16}{m+3} by \frac{m-4}{2m+6} by multiplying \frac{m^{2}-16}{m+3} by the reciprocal of \frac{m-4}{2m+6}.

$$\frac{\left(m^{2}-16\right)\left(2m+6\right)}{\left(m+3\right)\left(m-4\right)}$$

Factor the expressions that are not already factored.

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

Cancel out \left(m-4\right)\left(m+3\right) in both numerator and denominator.

$$2\left(m+4\right)$$

Expand the expression.

$$2m+8$$