# How do you simplify \frac { 2} { x } + \frac { 5} { 3}?

Oct 19, 2017

$\frac{5 x + 6}{3 x}$

#### Explanation:

In order to add fractions, we want them to have a common denominator. To do this, we will multiply the first fraction by $\frac{3}{3}$. This is simply another form of 1, but it will enable us to obtain a common denominator when we also multiply the second fraction by $\frac{x}{x}$, which again is equal to 1. Since we are multiplying by forms of 1, we are not changing the problem.

$\frac{2}{x} + \frac{5}{3} = \frac{2}{x} \left(\frac{3}{3}\right) + \frac{5}{3} \left(\frac{x}{x}\right) = \frac{2 \cdot 3}{x \cdot 3} + \frac{5 \cdot x}{3 \cdot x} = \frac{6}{3 x} + \frac{5 x}{3 x} = \frac{5 x + 6}{3 x}$

Oct 19, 2017

2/x+5/3=color(blue)((6+5x)/(3x)

#### Explanation:

Simpllfy:

$\frac{2}{x} + \frac{5}{3}$

In order to add or subtract fractions, they must have the same denominator. Multiply the denominators to get the least common denominator (LCD):

LCD$=$$x \times 3 = 3 x$

Multiply both fractions by a fraction form of $1$, so that each fraction has the denominator $3 x$. An example is $\frac{5}{5} = 1$. Multiiplying by fraction form of $1$ makes sure that the values do not change.

$\frac{2}{x} \times \frac{\textcolor{t e a l}{3}}{\textcolor{t e a l}{3}} + \frac{5}{3} \times \frac{\textcolor{m a \ge n t a}{x}}{\textcolor{m a \ge n t a}{x}}$

Simplify.

$\frac{6}{3 x} + \frac{5 x}{3 x}$

Simplify.

$\frac{6 + 5 x}{3 x}$