Question

How do you simplify `-4x \div \frac { x ^ { 2} } { 10}`?

Answer 1

`-4x div(x^2)/10=color(red)(-40/x)`

Explanation:

Remember that `color(green)a div (color(blue)b)/(color(magenta)c)` is the same as `color(green)a xx (color(magenta)c)/(color(blue)b)`

So
`color(white)("XXX")color(green)(-4x)div(color(blue)(x^2))/(color(magenta)(10)`
`color(white)("XXXXXXXXX")= color(green)(-4x) xx(color(magenta)(10))/(color(blue)(x^2)`

`color(white)("XXXXXXXXX")=(color(green)(-4 xx x)xxcolor(magenta)(10))/(color(blue)(x xx x)`

`color(white)("XXXXXXXXX")=-40/x`

Answer 2

See a solution process below:

Explanation:

First, rewrite the expression as:

`(-4x)/1 -: x^2/10`

Now, use this rule for dividing fractions to simplify 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)(-4x)/color(blue)(1))/(color(green)(x^2)/color(purple)(10)) => (color(red)(-4x) xx color(purple)(10))/(color(blue)(1) xx color(green)(x^2)) => (color(red)(-4color(black)(cancel(color(red)(x)))) xx color(purple)(10))/(color(blue)(1) xx cancel(color(green)(x^2))color(green)(x)) => -40/x`