Question

How do you simplify `(c/a+c/b) / (c/(ab))`?

Answer 1

`a+b`

Explanation:

[1]`color(white)("XXX")color(blue)((c/a+c/b) = (bc+ac)/(ab) = (c(a+b))/(ab))`

[2]`color(white)("XXX")color(blue)((c/a+c/b))/color(red)((c/(ab))) = color(blue)((c/a+c/b))*color(red)(((ab)/c))`

Substituting result [1] into [2]
`color(white)("XXX")color(blue)((c/a+c/b))/color(red)((c/(ab))) = color(blue)((c(a+b))/(ab))*color(red)((ab)/c)`

`color(white)("XXX")(c/a+c/b)/(c/(ab)) = (cancel(c)(a+b))/(cancel(ab))*(cancel(ab))/cancel(c) = a+b`