Question

How do you divide `\frac { ( x + 1) } { 4} \div \frac { x } { 4}`?

Answer 1

See a solution process below:

Explanation:

First, we can rewrite the expression as:

`((x + 1)/4)/(x/4)`

Now, we can use this rule for dividing fractions to divide the expression in the problem:

`(color(red)(a)/color(blue)(b))/(color(green)(c)/color(purple)(d)) = (color(red)(a) xx color(purple)(d))/(color(blue)(b) xx color(green)(c))`

`(color(red)((x + 1))/color(blue)(4))/(color(green)(x)/color(purple)(4)) => (color(red)((x + 1)) xx color(purple)(4))/(color(blue)(4) xx color(green)(x)) => (color(red)((x + 1)) xx cancel(color(purple)(4)))/(cancel(color(blue)(4)) xx color(green)(x)) =>`

`(x + 1)/x`

Or

`x/x + 1/x =>`

`1 + 1/x`

Answer 2

`(x+1)/x`

Explanation:

`(x+1)/4 div x/4`

Dividing is the same as multiplying by the reciprocal.

`(x+1)/cancel4 xx cancel4/x" "larr` cancel

`=(x+1)/x`

This cannot be simplified further.