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

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{m-2}{m-2}.

$$\frac{\frac{m^{2}-9}{3m^{2}-6m}}{\frac{m-2}{m-2}-\frac{1}{m-2}}$$

Since \frac{m-2}{m-2} and \frac{1}{m-2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{m^{2}-9}{3m^{2}-6m}}{\frac{m-2-1}{m-2}}$$

Combine like terms in m-2-1.

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

Divide \frac{m^{2}-9}{3m^{2}-6m} by \frac{m-3}{m-2} by multiplying \frac{m^{2}-9}{3m^{2}-6m} by the reciprocal of \frac{m-3}{m-2}.

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

Factor the expressions that are not already factored.

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

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

$$\frac{m+3}{3m}$$

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{m-2}{m-2}.

$$\frac{\frac{m^{2}-9}{3m^{2}-6m}}{\frac{m-2}{m-2}-\frac{1}{m-2}}$$

Since \frac{m-2}{m-2} and \frac{1}{m-2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{m^{2}-9}{3m^{2}-6m}}{\frac{m-2-1}{m-2}}$$

Combine like terms in m-2-1.

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

Divide \frac{m^{2}-9}{3m^{2}-6m} by \frac{m-3}{m-2} by multiplying \frac{m^{2}-9}{3m^{2}-6m} by the reciprocal of \frac{m-3}{m-2}.

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

Factor the expressions that are not already factored.

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

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

$$\frac{m+3}{3m}$$