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

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

Evaluate

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

Short Solution Steps

Multiply \frac{1}{4} and 1 to get \frac{1}{4}.

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

Multiply \frac{1}{4} times \frac{2a}{a^{2}-4} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 2 in both numerator and denominator.

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

Factor 2\left(a^{2}-4\right).

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

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

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

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

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

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

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

Combine like terms in a-2a-4.

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

Expand 2\left(a-2\right)\left(a+2\right).

$$\frac{-a-4}{2a^{2}-8}$$

Factor

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