To calculate: The simplified form of the rational expression -frac{15tu^{5}v}{3t^{3}u} and state the restrictions on the variable t, u.

To calculate: The simplified form of the rational expression $-\frac{15t{u}^{5}v}{3t^{3}u}is-\frac{5u^{4}v}{t^2}$
and restrictions on the variable is $t\ne 0,u\ne 0.$
Given Information:
The provided rational expression is $-\frac{15t{u}^{5}v}{3t^{3}u}.$
Formula used:
If, a, b, and c represent real valued expression, then $\frac{ac}{bc}=\frac{a}{b}forb\ne 0,c\ne 0.$ Calculation:
Consider the rational expression, $-\frac{15t{u}^{5}v}{3t^{3}u}$
Now,
Take common 3tu from the numerator and denominator from the provided rational expression,
$-\frac{15t{u}^{5}v}{3t^{3}u}$
Apply,
if a,b, and c represent real valued expression, then $\frac{ac}{bc}=\frac{a}{b}forb\ne 0,c\ne 0.$
Therefore,
$-\frac{15t{u}^{5}v}{3t^{3}u}=-\frac{\text{⧸}3tu(5u^{4}v)}{\text{⧸}3tu(t^2)}$
Here,
$t\ne 0,u\ne 0$
Therefore,
The simplified rational expression $-\frac{15t{u}^{5}v}{3t^{3}u}is\frac{5u^{4}v}{t^2}$
and restrictions on the variable is $t\ne 0,u\ne 0.$