Question

How do you simplify `(4x+16)/x div (x+4)`?

Answer 1

`4/x`

Explanation:

This is the same as `(4x+16)/x xx1/(x+4)` giving

`(4x+16)/(x(x+4))`

Factor out 4 from the top giving:

`(4(x+4))/(x(x+4)) color(white)("d") ->color(white)("d")4/x xx (x+4)/(x+4)`

But `(x+4)/(x+4)=1` giving

`color(white)("ddddddddd") -> color(white)("d")4/x color(white)("d") xx color(white)("d")1 = 4/x`

Answer 2

`4/x`

Explanation:

With algebraic fractions,a good place to start is to factorise if possible.

`(4x+16)/x div (x+4)`

`=(4(x+4))/x xx 1/((x+4))" "larr` multiply and invert

Now you can cancel the factors - there is a multiplication sign between them.

`=(4cancel((x+4)))/x xx 1/cancel((x+4))`

`=4/x`