Question

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

Answer 1

Basic principles

Explanation:

Fractions are called rational numbers because they can be expressed in the form of `a/b`

Counting numbers are also rational numbers. There form of `a/b` is:

`1/1, 2/1, 3/1......`
,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The bottom number is the size indicator of what you are counting.

In that
`1/2` requires 2 of them to make a whole but there is a count of 1

`2/5` requires 5 of them to make a whole but you have a count of 2

`color(blue)("You can only directly add or subtract the 'counts' if")`
`color(blue)("if the size indicators are the same")`

`color(brown)("This is why you can directly add "3/1+2/1=5/1)`
`color(brown)("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 `2x^2`

ADDING THE COUNTS DOES NOT CHANGE THE SIZE INDICATOR!