Solve (3/a-2+2/a+2)*(a^2-4)

$$( \frac { 3 } { a - 2 } + \frac { 2 } { a + 2 } ) \cdot ( a ^ { 2 } - 4 )$$

Evaluate

$$5a+2$$

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{3}{a-2} times \frac{a+2}{a+2}. Multiply \frac{2}{a+2} times \frac{a-2}{a-2}.

$$\left(\frac{3\left(a+2\right)}{\left(a-2\right)\left(a+2\right)}+\frac{2\left(a-2\right)}{\left(a-2\right)\left(a+2\right)}\right)\left(a^{2}-4\right)$$

Since \frac{3\left(a+2\right)}{\left(a-2\right)\left(a+2\right)} and \frac{2\left(a-2\right)}{\left(a-2\right)\left(a+2\right)} have the same denominator, add them by adding their numerators.

$$\frac{3\left(a+2\right)+2\left(a-2\right)}{\left(a-2\right)\left(a+2\right)}\left(a^{2}-4\right)$$

Do the multiplications in 3\left(a+2\right)+2\left(a-2\right).

$$\frac{3a+6+2a-4}{\left(a-2\right)\left(a+2\right)}\left(a^{2}-4\right)$$

Combine like terms in 3a+6+2a-4.

$$\frac{5a+2}{\left(a-2\right)\left(a+2\right)}\left(a^{2}-4\right)$$

Express \frac{5a+2}{\left(a-2\right)\left(a+2\right)}\left(a^{2}-4\right) as a single fraction.

$$\frac{\left(5a+2\right)\left(a^{2}-4\right)}{\left(a-2\right)\left(a+2\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(a-2\right)\left(a+2\right)\left(5a+2\right)}{\left(a-2\right)\left(a+2\right)}$$

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

$$5a+2$$

Expand

$$5a+2$$

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{3}{a-2} times \frac{a+2}{a+2}. Multiply \frac{2}{a+2} times \frac{a-2}{a-2}.

$$\left(\frac{3\left(a+2\right)}{\left(a-2\right)\left(a+2\right)}+\frac{2\left(a-2\right)}{\left(a-2\right)\left(a+2\right)}\right)\left(a^{2}-4\right)$$

Since \frac{3\left(a+2\right)}{\left(a-2\right)\left(a+2\right)} and \frac{2\left(a-2\right)}{\left(a-2\right)\left(a+2\right)} have the same denominator, add them by adding their numerators.

$$\frac{3\left(a+2\right)+2\left(a-2\right)}{\left(a-2\right)\left(a+2\right)}\left(a^{2}-4\right)$$

Do the multiplications in 3\left(a+2\right)+2\left(a-2\right).

$$\frac{3a+6+2a-4}{\left(a-2\right)\left(a+2\right)}\left(a^{2}-4\right)$$

Combine like terms in 3a+6+2a-4.

$$\frac{5a+2}{\left(a-2\right)\left(a+2\right)}\left(a^{2}-4\right)$$

Express \frac{5a+2}{\left(a-2\right)\left(a+2\right)}\left(a^{2}-4\right) as a single fraction.

$$\frac{\left(5a+2\right)\left(a^{2}-4\right)}{\left(a-2\right)\left(a+2\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(a-2\right)\left(a+2\right)\left(5a+2\right)}{\left(a-2\right)\left(a+2\right)}$$

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

$$5a+2$$