Question

I need to solve for p and have a rationalized denominator

Answer 1

Answer:

$p = \pm \dfrac{\sqrt{r(st - 1)}}{st - 1}$

or

$p = \dfrac{\sqrt{r(st - 1)}}{st - 1}$

Step-by-step explanation:

$t = \dfrac{p^2 + r}{p^2s}$

$p^2st = p^2 + r$

$p^2st - p^2 = r$

$p^2(st - 1) = r$

$p^2 = \dfrac{r}{st - 1}$

$p = \pm \sqrt{\dfrac{r}{st - 1}}$

Your picture cuts out the assumption. If the assumption is that all variables are non-negative, then the answer is

$p = \sqrt{\dfrac{r}{st - 1}}$

$p = \dfrac{\sqrt{r}}{\sqrt{st - 1}}}$

$p = \dfrac{\sqrt{r}}{\sqrt{st - 1}}} \times \dfrac{\sqrt{st - 1}}{\sqrt{st - 1}}$

$p = \dfrac{\sqrt{r} \sqrt{st - 1}}{\sqrt{st - 1}\sqrt{st - 1}}$

$p = \dfrac{\sqrt{r(st - 1)}}{st - 1}$