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

1 Answer
Dec 26, 2017

#{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}#