Solve 4/a^2-4-1/a-2

$$\frac { 4 } { a ^ { 2 } - 4 } - \frac { 1 } { a - 2 }$$

Evaluate

$$-\frac{1}{a+2}$$

Short Solution Steps

Factor a^{2}-4.

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

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

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

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

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

Do the multiplications in 4-\left(a+2\right).

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

Combine like terms in 4-a-2.

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

Extract the negative sign in 2-a.

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

Cancel out a-2 in both numerator and denominator.

$$\frac{-1}{a+2}$$

Differentiate w.r.t. a

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