Solve left(1/a+2+1/a-2right)a^2-4/2a

$$\left( \frac{ 1 }{ a+2 } + \frac{ 1 }{ a-2 } \right) \frac{ { a }^{ 2 } -4 }{ 2a }$$

Evaluate

$$1$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a+2 and a-2 is \left(a-2\right)\left(a+2\right). Multiply \frac{1}{a+2} times \frac{a-2}{a-2}. Multiply \frac{1}{a-2} times \frac{a+2}{a+2}.

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

Since \frac{a-2}{\left(a-2\right)\left(a+2\right)} and \frac{a+2}{\left(a-2\right)\left(a+2\right)} have the same denominator, add them by adding their numerators.

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

Combine like terms in a-2+a+2.

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

Multiply \frac{2a}{\left(a-2\right)\left(a+2\right)} times \frac{a^{2}-4}{2a} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 2a in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

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

$$1$$

Factor

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