Solve (m-2/m+2-m+2/m-2):8m/m^2-4

$$( \frac { m - 2 } { m + 2 } - \frac { m + 2 } { m - 2 } ) : \frac { 8 m } { m ^ { 2 } - 4 }$$

Evaluate

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Short Solution Steps

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

$$\frac{\frac{\left(m-2\right)\left(m-2\right)}{\left(m-2\right)\left(m+2\right)}-\frac{\left(m+2\right)\left(m+2\right)}{\left(m-2\right)\left(m+2\right)}}{\frac{8m}{m^{2}-4}}$$

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

$$\frac{\frac{\left(m-2\right)\left(m-2\right)-\left(m+2\right)\left(m+2\right)}{\left(m-2\right)\left(m+2\right)}}{\frac{8m}{m^{2}-4}}$$

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

$$\frac{\frac{m^{2}-2m-2m+4-m^{2}-2m-2m-4}{\left(m-2\right)\left(m+2\right)}}{\frac{8m}{m^{2}-4}}$$

Combine like terms in m^{2}-2m-2m+4-m^{2}-2m-2m-4.

$$\frac{\frac{-8m}{\left(m-2\right)\left(m+2\right)}}{\frac{8m}{m^{2}-4}}$$

Divide \frac{-8m}{\left(m-2\right)\left(m+2\right)} by \frac{8m}{m^{2}-4} by multiplying \frac{-8m}{\left(m-2\right)\left(m+2\right)} by the reciprocal of \frac{8m}{m^{2}-4}.

$$\frac{-8m\left(m^{2}-4\right)}{\left(m-2\right)\left(m+2\right)\times 8m}$$

Cancel out 8m in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

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

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Factor

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