Solve a^2-4/a^2+4adiva^2-2a/a+4

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

Evaluate

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

Short Solution Steps

Divide \frac{a^{2}-4}{a^{2}+4a} by \frac{a^{2}-2a}{a+4} by multiplying \frac{a^{2}-4}{a^{2}+4a} by the reciprocal of \frac{a^{2}-2a}{a+4}.

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

Factor the expressions that are not already factored.

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

Cancel out \left(a-2\right)\left(a+4\right) in both numerator and denominator.

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

Expand

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

Short Solution Steps

Divide \frac{a^{2}-4}{a^{2}+4a} by \frac{a^{2}-2a}{a+4} by multiplying \frac{a^{2}-4}{a^{2}+4a} by the reciprocal of \frac{a^{2}-2a}{a+4}.

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

Factor the expressions that are not already factored.

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

Cancel out \left(a-2\right)\left(a+4\right) in both numerator and denominator.

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