Question

How do you add, simplify and state the domain of `(t^2s)/(rs)+(rs^2)/(rt)`?

Answer 1

`{t^3+s^2r}/{tr}`

Explanation:

You need to use "Lowest Common Denominator":
`{t^2color(green)(s)}/{rcolor(green)(s)}+{color(red)(r)s^2}/{color(red)(r)t}=?`
First step, if `s!=0` and `r!=0` you may cancel `color(green)(s)` and `color(red)(r)`
`=>`
`{t^2cancel(color(green)(s))}/{rcancel(color(green)(s))}+{cancel(color(red)(r))s^2}/{cancel(color(red)(r))t}={t^2}/{r}+{s^2}/{t}=?`
Now we can see that `rt` is the lowest common denominator:
`{t^2color(orange)(t)}/{rcolor(orange)(t)}+{s^2color(orange)(r)}/{tcolor(orange)(r)}={t^3+s^2r}/{tr}`