# How can you evaluate (k-4h+2)/(2k)+(4k+3h-1)/(7k)?

Aug 14, 2015

$\frac{15 k - 22 h + 12}{14 k}$

#### Explanation:

Notice that you need to add two fractions, one that has the denominator equal to $2 k$, and the other one that has the denominator equal to $7 k$.

Right from the start, the first thing that you need to do is find the common denominator, which in your case is $14 k$.

To get both fractions to have the same denominator, multiply the first one by $\frac{7}{7}$ and the second one by $\frac{2}{2}$. This will get you

$\frac{7 \cdot \left(k - 4 h + 2\right)}{7 \cdot 2 k} + \frac{2 \cdot \left(4 k + 3 h - 1\right)}{2 \cdot 7 k}$

$\frac{7 k - 28 h + 14}{14 k} + \frac{8 k + 6 h - 2}{14 k}$

Now simply add the two numerators to get

$\frac{7 k - 28 h + 14 + 8 k + 6 h - 2}{14 k}$

To simplify this fraction, combine like terms

$\frac{7 k + 8 k - 28 h + 6 h + 14 - 2}{14 k}$

$\textcolor{g r e e n}{\frac{15 k - 22 h + 12}{14 k}}$