Question

How do you simplify `(15a+5b)/(5ab) div 3a+b`?

Answer 1

`(15a+5b)/(5ab) div (3a+b) = 1/(ab)`
`color(white)("XXXX")`Warning: this is not exactly what was asked, but I think it was what was intended.

Explanation:

`(15a+5b)/(5ab) div (3a+b)`

`color(white)("XXXX")` `=(15a+5b)/(5ab) xx 1/(3a+b)`

`color(white)("XXXX")` `= (5(3a+b))/(5(ab)) xx 1/(3a+b)`

`color(white)("XXXX")` `= (cancel(5)(cancel(3a+b)))/(cancel(5)(ab)) xx 1/(cancel(3a+b))`

`color(white)("XXXX")` `=1/(ab)`

Technically what was asked should have been evaluated as
`color(white)("XXXX")` `((15a+5b)/(5ab) xx 1/(3a)) + 2`
Please repost, if that is what you intended.