# How do you combine 1/(2x^2)-5/(2x^2)?

Jul 24, 2016

Basic principles

#### Explanation:

Fractions are called rational numbers because they can be expressed in the form of $\frac{a}{b}$

Counting numbers are also rational numbers. There form of $\frac{a}{b}$ is:

$\frac{1}{1} , \frac{2}{1} , \frac{3}{1.} \ldots . .$
,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The bottom number is the size indicator of what you are counting.

In that
$\frac{1}{2}$ requires 2 of them to make a whole but there is a count of 1

$\frac{2}{5}$ requires 5 of them to make a whole but you have a count of 2

$\textcolor{b l u e}{\text{You can only directly add or subtract the 'counts' if}}$
$\textcolor{b l u e}{\text{if the size indicators are the same}}$

$\textcolor{b r o w n}{\text{This is why you can directly add } \frac{3}{1} + \frac{2}{1} = \frac{5}{1}}$
$\textcolor{b r o w n}{\text{People do not write the denominators of 1}}$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(green)(1/(2x^2)-5/(2x^2)" have the same size indicator!"

Directly adding the counts give a count of $1 + 5 = 6$ and the size indicator (DENOMINATOR) is $2 {x}^{2}$

ADDING THE COUNTS DOES NOT CHANGE THE SIZE INDICATOR!