Solve 3a/a+2-a-4b/2

$$\frac { 3 a } { a + 2 } - \frac { a - 4 b } { 2 }$$

Evaluate

$$\frac{8b+4a+4ab-a^{2}}{2\left(a+2\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a+2 and 2 is 2\left(a+2\right). Multiply \frac{3a}{a+2} times \frac{2}{2}. Multiply \frac{a-4b}{2} times \frac{a+2}{a+2}.

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

Since \frac{2\times 3a}{2\left(a+2\right)} and \frac{\left(a-4b\right)\left(a+2\right)}{2\left(a+2\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 2\times 3a-\left(a-4b\right)\left(a+2\right).

$$\frac{6a-a^{2}-2a+4ba+8b}{2\left(a+2\right)}$$

Combine like terms in 6a-a^{2}-2a+4ba+8b.

$$\frac{4a-a^{2}+4ba+8b}{2\left(a+2\right)}$$

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

$$\frac{4a-a^{2}+4ba+8b}{2a+4}$$

Expand

$$\frac{8b+4a+4ab-a^{2}}{2\left(a+2\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a+2 and 2 is 2\left(a+2\right). Multiply \frac{3a}{a+2} times \frac{2}{2}. Multiply \frac{a-4b}{2} times \frac{a+2}{a+2}.

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

Since \frac{2\times 3a}{2\left(a+2\right)} and \frac{\left(a-4b\right)\left(a+2\right)}{2\left(a+2\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 2\times 3a-\left(a-4b\right)\left(a+2\right).

$$\frac{6a-a^{2}-2a+4ba+8b}{2\left(a+2\right)}$$

Combine like terms in 6a-a^{2}-2a+4ba+8b.

$$\frac{4a-a^{2}+4ba+8b}{2\left(a+2\right)}$$

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

$$\frac{4a-a^{2}+4ba+8b}{2a+4}$$