Solve k+8/4k+8+k-a

$$\frac { k + 8 } { 4 k + 8 } + k - a$$

Evaluate

$$\frac{8+9k+4k^{2}-8a-4ak}{4\left(k+2\right)}$$

Short Solution Steps

Factor 4k+8.

$$\frac{k+8}{4\left(k+2\right)}+k-a$$

To add or subtract expressions, expand them to make their denominators the same. Multiply k-a times \frac{4\left(k+2\right)}{4\left(k+2\right)}.

$$\frac{k+8}{4\left(k+2\right)}+\frac{\left(k-a\right)\times 4\left(k+2\right)}{4\left(k+2\right)}$$

Since \frac{k+8}{4\left(k+2\right)} and \frac{\left(k-a\right)\times 4\left(k+2\right)}{4\left(k+2\right)} have the same denominator, add them by adding their numerators.

$$\frac{k+8+\left(k-a\right)\times 4\left(k+2\right)}{4\left(k+2\right)}$$

Do the multiplications in k+8+\left(k-a\right)\times 4\left(k+2\right).

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

Combine like terms in k+8+4k^{2}+8k-4ak-8a.

$$\frac{9k+8+4k^{2}-4ak-8a}{4\left(k+2\right)}$$

Expand 4\left(k+2\right).

$$\frac{9k+8+4k^{2}-4ak-8a}{4k+8}$$

Expand

$$-\frac{4ak+8a-4k^{2}-9k-8}{4\left(k+2\right)}$$

Short Solution Steps

Factor 4k+8.

$$\frac{k+8}{4\left(k+2\right)}+k-a$$

To add or subtract expressions, expand them to make their denominators the same. Multiply k-a times \frac{4\left(k+2\right)}{4\left(k+2\right)}.

$$\frac{k+8}{4\left(k+2\right)}+\frac{\left(k-a\right)\times 4\left(k+2\right)}{4\left(k+2\right)}$$

Since \frac{k+8}{4\left(k+2\right)} and \frac{\left(k-a\right)\times 4\left(k+2\right)}{4\left(k+2\right)} have the same denominator, add them by adding their numerators.

$$\frac{k+8+\left(k-a\right)\times 4\left(k+2\right)}{4\left(k+2\right)}$$

Do the multiplications in k+8+\left(k-a\right)\times 4\left(k+2\right).

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

Combine like terms in k+8+4k^{2}+8k-4ak-8a.

$$\frac{9k+8+4k^{2}-4ak-8a}{4\left(k+2\right)}$$

Expand 4\left(k+2\right).

$$\frac{9k+8+4k^{2}-4ak-8a}{4k+8}$$