Answer:
[tex] p = \pm \dfrac{\sqrt{r(st - 1)}}{st - 1} [/tex]
or
[tex] p = \dfrac{\sqrt{r(st - 1)}}{st - 1} [/tex]
Step-by-step explanation:
[tex] t = \dfrac{p^2 + r}{p^2s} [/tex]
[tex] p^2st = p^2 + r [/tex]
[tex] p^2st - p^2 = r [/tex]
[tex] p^2(st - 1) = r [/tex]
[tex] p^2 = \dfrac{r}{st - 1} [/tex]
[tex] p = \pm \sqrt{\dfrac{r}{st - 1}} [/tex]
Your picture cuts out the assumption. If the assumption is that all variables are non-negative, then the answer is
[tex] p = \sqrt{\dfrac{r}{st - 1}} [/tex]
[tex] p = \dfrac{\sqrt{r}}{\sqrt{st - 1}}} [/tex]
[tex] p = \dfrac{\sqrt{r}}{\sqrt{st - 1}}} \times \dfrac{\sqrt{st - 1}}{\sqrt{st - 1}} [/tex]
[tex] p = \dfrac{\sqrt{r} \sqrt{st - 1}}{\sqrt{st - 1}\sqrt{st - 1}} [/tex]
[tex] p = \dfrac{\sqrt{r(st - 1)}}{st - 1} [/tex]
