Solve -2m/(m-3)^2div(1/m-3-1/m+3)

$$\frac { - 2 m } { ( m - 3 ) ^ { 2 } } \div ( \frac { 1 } { m - 3 } - \frac { 1 } { m + 3 } )$$

Evaluate

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

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}.

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

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.

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

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

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

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

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

Divide \frac{-2m}{\left(m-3\right)^{2}} by \frac{6}{\left(m-3\right)\left(m+3\right)} by multiplying \frac{-2m}{\left(m-3\right)^{2}} by the reciprocal of \frac{6}{\left(m-3\right)\left(m+3\right)}.

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

Cancel out 2\left(m-3\right) in both numerator and denominator.

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

Cancel out -1 in both numerator and denominator.

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

Use the distributive property to multiply m by m+3.

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

Use the distributive property to multiply -3 by m-3.

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

Expand

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

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}.

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

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.

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

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

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

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

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

Divide \frac{-2m}{\left(m-3\right)^{2}} by \frac{6}{\left(m-3\right)\left(m+3\right)} by multiplying \frac{-2m}{\left(m-3\right)^{2}} by the reciprocal of \frac{6}{\left(m-3\right)\left(m+3\right)}.

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

Cancel out 2\left(m-3\right) in both numerator and denominator.

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

Cancel out -1 in both numerator and denominator.

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

Use the distributive property to multiply m by m+3.

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

Use the distributive property to multiply -3 by m-3.

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