Answer:
k = [tex]\frac{u^2y-x}{u^2-1}[/tex]
Step-by-step explanation:
Given
u = [tex]\sqrt{\frac{k-x}{k-y} }[/tex] ( square both sides )
u² = [tex]\frac{k-x}{k-y}[/tex] ← multiply both sides by (k - y)
u²(k - y) = k - x ← distribute left side
u²k - u²y = k - x ( subtract k from both sides )
u²k - k - u²y = - x ( add u²y to both sides )
u²k - k = u²y - x ← factor out k from each term on the left side
k(u² - 1) = u²y - x ← divide both sides by (u² - 1)
k = [tex]\frac{u^2y-x}{u^2-1}[/tex]
