Solve 1/m-3-1/m+3-6-2m/left(m-3right)^2

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

Evaluate

$$\frac{2\left(m+6\right)}{m^{2}-9}$$

Short Solution Steps

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

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

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

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

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

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

Combine like terms in m+3-m+3.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(m-3\right)\left(m+3\right) and \left(m-3\right)^{2} is \left(m+3\right)\left(m-3\right)^{2}. Multiply \frac{6}{\left(m-3\right)\left(m+3\right)} times \frac{m-3}{m-3}. Multiply \frac{6-2m}{\left(m-3\right)^{2}} times \frac{m+3}{m+3}.

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

Since \frac{6\left(m-3\right)}{\left(m+3\right)\left(m-3\right)^{2}} and \frac{\left(6-2m\right)\left(m+3\right)}{\left(m+3\right)\left(m-3\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 6\left(m-3\right)-\left(6-2m\right)\left(m+3\right).

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

Combine like terms in 6m-18-6m-18+2m^{2}+6m.

$$\frac{6m-36+2m^{2}}{\left(m+3\right)\left(m-3\right)^{2}}$$

Factor the expressions that are not already factored in \frac{6m-36+2m^{2}}{\left(m+3\right)\left(m-3\right)^{2}}.

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

Cancel out m-3 in both numerator and denominator.

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

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

$$\frac{2\left(m+6\right)}{m^{2}-9}$$

Use the distributive property to multiply 2 by m+6.

$$\frac{2m+12}{m^{2}-9}$$

Expand

$$\frac{2\left(m+6\right)}{m^{2}-9}$$

Short Solution Steps

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

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

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

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

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

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

Combine like terms in m+3-m+3.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(m-3\right)\left(m+3\right) and \left(m-3\right)^{2} is \left(m+3\right)\left(m-3\right)^{2}. Multiply \frac{6}{\left(m-3\right)\left(m+3\right)} times \frac{m-3}{m-3}. Multiply \frac{6-2m}{\left(m-3\right)^{2}} times \frac{m+3}{m+3}.

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

Since \frac{6\left(m-3\right)}{\left(m+3\right)\left(m-3\right)^{2}} and \frac{\left(6-2m\right)\left(m+3\right)}{\left(m+3\right)\left(m-3\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 6\left(m-3\right)-\left(6-2m\right)\left(m+3\right).

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

Combine like terms in 6m-18-6m-18+2m^{2}+6m.

$$\frac{6m-36+2m^{2}}{\left(m+3\right)\left(m-3\right)^{2}}$$

Factor the expressions that are not already factored in \frac{6m-36+2m^{2}}{\left(m+3\right)\left(m-3\right)^{2}}.

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

Cancel out m-3 in both numerator and denominator.

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

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

$$\frac{2\left(m+6\right)}{m^{2}-9}$$

Use the distributive property to multiply 2 by m+6.

$$\frac{2m+12}{m^{2}-9}$$