Question

How do you combine `1/2+2/(x+2)`?

Answer 1

`(x+6)/(2x+4)`

Explanation:

A fraction consists of

`("numerator")/("denominator") -> ("count")/("size indicator of what you are counting")`

`color(blue)("Important fact 1")`
You can not DIRECTLY add or subtract the counts unless the size indicators are the same

`color(blue)("Important fact 2")`
Multiply by 1 and you do not change the value. However, 1 comes in many forms so you can change the way numbers look but not change their actual value.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)([1/2color(red)(xx1)]+[2/(x+2)color(red)(xx1)]`

Is the same as:

`color(blue)([1/2color(red)(xx(x+2)/(x+2))]+[2/(x+2)color(red)(xx2/2)]`

`(x+2)/(2(x+2))+4/(2(x+2))`

`(x+2+4)/(2(x+2)) " "=" "(x+6)/(2x+4)`