# How do you add \frac { 5x + 4} { 2x } + \frac { 2x + 1} { 3x }?

Mar 4, 2017

See the entire solution process below:

#### Explanation:

To add fractions the two fractions need to be over common denominators. In this case, we can use a common denominator of $6 x$. To get each fraction over the common denominator of $6 x$ we must multiply each fraction by the appropriate form of $1$:

$\left(\frac{3}{3} \times \frac{5 x + 4}{2 x}\right) + \left(\frac{2}{2} \times \frac{2 x + 1}{3 x}\right)$

$\left(\frac{3 \left(5 x + 4\right)}{3 \times 2 x}\right) + \left(\frac{2 \left(2 x + 1\right)}{2 \times 3 x}\right)$

$\frac{\left(3 \times 5 x\right) + \left(3 \times 4\right)}{6 x} + \frac{\left(2 \times 2 x\right) + \left(2 \times 1\right)}{6 x}$

$\frac{15 x + 12}{6 x} + \frac{4 x + 2}{6 x}$

We can next add the numerators of the two fractions:

$\frac{15 x + 12 + 4 x + 2}{6 x}$

We can now group and combine like terms in the numerator:

$\frac{15 x + 4 x + 12 + 2}{6 x}$

$\frac{19 x + 14}{6 x}$