# How do you simplify fractions with variables?

May 19, 2016

See explanation

#### Explanation:

This is one of those question that matches the phrase: "how long is a piece of string"! It all depends on the expression/equation content and format.

Consider the example: $\frac{2}{a} + \frac{3}{a b}$

When adding fractions directly the denominator (size indicator of what you are counting) has to be the same. Then you can directly add the numerators (the counts)

Making the denominators the same

Multiply $\frac{2}{a}$ by 1 but in the form of $1 = \frac{b}{b}$

$\implies \frac{2}{a} \times \frac{b}{b} = \frac{2 b}{a b}$

So $\text{ "color(brown)(2/a+3/(ab))" "color(blue)(->" } \frac{2 b}{a b} + \frac{3}{a b} \to \frac{2 b + 3}{a b}$

$\textcolor{red}{\text{So some would consider:}}$

$\textcolor{red}{\frac{2}{a} + \frac{3}{a b} \text{ as the simplified version of } \frac{2 b + 3}{a b}}$