Solve (a/a-2-4/a^2-2a)diva+2/a

$$( \frac { a } { a - 2 } - \frac { 4 } { a ^ { 2 } - 2 a } ) \div \frac { a + 2 } { a }$$

Evaluate

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Short Solution Steps

Factor a^{2}-2a.

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

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

$$\frac{\frac{aa}{a\left(a-2\right)}-\frac{4}{a\left(a-2\right)}}{\frac{a+2}{a}}$$

Since \frac{aa}{a\left(a-2\right)} and \frac{4}{a\left(a-2\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{aa-4}{a\left(a-2\right)}}{\frac{a+2}{a}}$$

Do the multiplications in aa-4.

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

Factor the expressions that are not already factored in \frac{a^{2}-4}{a\left(a-2\right)}.

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

Cancel out a-2 in both numerator and denominator.

$$\frac{\frac{a+2}{a}}{\frac{a+2}{a}}$$

Divide \frac{a+2}{a} by \frac{a+2}{a} by multiplying \frac{a+2}{a} by the reciprocal of \frac{a+2}{a}.

$$\frac{\left(a+2\right)a}{a\left(a+2\right)}$$

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

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Factor

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