# How do you simplify 7/(4k+8)-k/(k+2)?

Jun 3, 2017

See a solution process below:

#### Explanation:

To be able to add or subtract fractions, both fractions must be over a common denominator. In this case $\left(4 k + 8\right)$. We can put the fraction on the right over this common denominator by multiplying the fraction by the appropriate form of $1$:

$\frac{7}{4 k + 8} - \left(\frac{4}{4} \times \frac{k}{k + 2}\right) \implies$

$\frac{7}{4 k + 8} - \frac{4 k}{4 \left(k + 2\right)} \implies$

$\frac{7}{4 k + 8} - \frac{4 k}{\left(4 \cdot k\right) + \left(4 \cdot 2\right)} \implies$

$\frac{7}{4 k + 8} - \frac{4 k}{4 k + 8}$

We can now subtract the numerators over the common denominator:

$\frac{7}{4 k + 8} - \frac{4 k}{4 k + 8} \implies$

$\frac{7 - 4 k}{4 k + 8}$