Solve 6-2m/m^2-6m+9div(1/m-3-1/m+3)

$$\frac { 6 - 2 m } { m ^ { 2 } - 6 m + 9 } \div ( \frac { 1 } { m - 3 } - \frac { 1 } { m + 3 } )$$

Evaluate

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

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}.

$$\frac{\frac{6-2m}{m^{2}-6m+9}}{\frac{m+3}{\left(m-3\right)\left(m+3\right)}-\frac{m-3}{\left(m-3\right)\left(m+3\right)}}$$

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.

$$\frac{\frac{6-2m}{m^{2}-6m+9}}{\frac{m+3-\left(m-3\right)}{\left(m-3\right)\left(m+3\right)}}$$

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

$$\frac{\frac{6-2m}{m^{2}-6m+9}}{\frac{m+3-m+3}{\left(m-3\right)\left(m+3\right)}}$$

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

$$\frac{\frac{6-2m}{m^{2}-6m+9}}{\frac{6}{\left(m-3\right)\left(m+3\right)}}$$

Divide \frac{6-2m}{m^{2}-6m+9} by \frac{6}{\left(m-3\right)\left(m+3\right)} by multiplying \frac{6-2m}{m^{2}-6m+9} by the reciprocal of \frac{6}{\left(m-3\right)\left(m+3\right)}.

$$\frac{\left(6-2m\right)\left(m-3\right)\left(m+3\right)}{\left(m^{2}-6m+9\right)\times 6}$$

Factor the expressions that are not already factored.

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

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

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

Expand the expression.

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

Factor the expressions that are not already factored.

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

Cancel out m-3 in both numerator and denominator.

$$\frac{-m-3}{3}$$

Expand

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

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}.

$$\frac{\frac{6-2m}{m^{2}-6m+9}}{\frac{m+3}{\left(m-3\right)\left(m+3\right)}-\frac{m-3}{\left(m-3\right)\left(m+3\right)}}$$

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.

$$\frac{\frac{6-2m}{m^{2}-6m+9}}{\frac{m+3-\left(m-3\right)}{\left(m-3\right)\left(m+3\right)}}$$

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

$$\frac{\frac{6-2m}{m^{2}-6m+9}}{\frac{m+3-m+3}{\left(m-3\right)\left(m+3\right)}}$$

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

$$\frac{\frac{6-2m}{m^{2}-6m+9}}{\frac{6}{\left(m-3\right)\left(m+3\right)}}$$

Divide \frac{6-2m}{m^{2}-6m+9} by \frac{6}{\left(m-3\right)\left(m+3\right)} by multiplying \frac{6-2m}{m^{2}-6m+9} by the reciprocal of \frac{6}{\left(m-3\right)\left(m+3\right)}.

$$\frac{\left(6-2m\right)\left(m-3\right)\left(m+3\right)}{\left(m^{2}-6m+9\right)\times 6}$$

Factor the expressions that are not already factored.

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

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

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

Expand the expression.

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

Factor the expressions that are not already factored.

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

Cancel out m-3 in both numerator and denominator.

$$\frac{-m-3}{3}$$