Question

How do you evaluate `\frac{x-9}{4}\div \frac{x}{8}`?

Answer 1

See a solution process below:

Explanation:

First, rewrite the expression as:

`((x - 9)/4)/(x/8)`

Now, use this rule for dividing fractions to evaluate the expression:

`(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 - 9))/color(blue)(4))/(color(green)(x)/color(purple)(8)) => (color(red)((x - 9)) xx color(purple)(8))/(color(blue)(4) xx color(green)(x)) => (color(red)((x - 9)) xx cancel(color(purple)(8))color(purple)(2))/(cancel(color(blue)(4)) xx color(green)(x)) =>`

`(color(purple)(2)color(red)((x - 9)))/color(green)(x) => ((color(purple)(2) xx color(red)(x)) - (color(purple)(2) xx color(red)(9)))/color(green)(x) =>`

`(2x - 18)/x`