Evaluate: P=sqrt((mx)/(t)-t^2x)

Expression: $P=\sqrt{ \frac{ mx }{ t }-{t}^{2}x }$

Write all numerators above the common denominator

$P=\sqrt{ \frac{ mx-{t}^{3}x }{ t } }$

Swap the sides of the equation

$\sqrt{ \frac{ mx-{t}^{3}x }{ t } }=P$

Square both sides of the equation

$\frac{ mx-{t}^{3}x }{ t }={P}^{2}$

Multiply both sides of the equation by $t$

$mx-{t}^{3}x=t{P}^{2}$

Factor out $x$ from the expression

$\left( m-{t}^{3} \right)x=t{P}^{2}$

Divide both sides of the equation by $m-{t}^{3}$

$x=\frac{ t{P}^{2} }{ m-{t}^{3} }$

Use the commutative property to reorder the terms

$x=\frac{ {P}^{2}t }{ m-{t}^{3} }$