Solve 3a^2/a^2-4-3a-2/a-2

$$\frac { 3 a ^ { 2 } } { a ^ { 2 } - 4 } - \frac { 3 a - 2 } { a - 2 }$$

Evaluate

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

Short Solution Steps

Factor a^{2}-4.

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

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

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

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

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

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

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

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

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

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

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

Expand

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

Short Solution Steps

Factor a^{2}-4.

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

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

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

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

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

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

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

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

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

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

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