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

Dec 26, 2017

$\frac{{t}^{3} + {s}^{2} r}{t r}$

#### 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 $s \ne 0$ and $r \ne 0$ you may cancel $\textcolor{g r e e n}{s}$ and $\textcolor{red}{r}$
$\implies$
{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 $r t$ is the lowest common denominator:
$\frac{{t}^{2} \textcolor{\mathmr{and} a n \ge}{t}}{r \textcolor{\mathmr{and} a n \ge}{t}} + \frac{{s}^{2} \textcolor{\mathmr{and} a n \ge}{r}}{t \textcolor{\mathmr{and} a n \ge}{r}} = \frac{{t}^{3} + {s}^{2} r}{t r}$