Question

How do you simplify `(5/(4x^2)) / (8/x^3)`?

Answer 1

`frac{frac{5}{4x^2}}{frac{8}{x^3}} = frac{5x}{32}`

Explanation:

Multiply the "lowest common multiple" to both the numerator and the denominator.

A nice common multiple of `4x^2` and `x^3` is `4x^3`.

So trying to multiply out

`frac{frac{5}{4x^2} * (4x^3)}{frac{8}{x^3} * (4x^3)} = frac{5x}{32}`

Answer 2

`(5x)/32`

Explanation:

When you have a fraction over a fraction, you can make use of the following as the first step in simplifying.

`(color(red)(a)/color(blue)(b))/(color(blue)(c)/color(red)(d)) = (color(red)(axxd))/(color(blue)(bxxc))`

`(5/(4x^2))/(8/x^3) = (5xxx^3)/(4x^2xx8)" "larr" simplify"`

=`(5x)/32`