x varies directly as the product of u and v and inversely as their sum….

x varies directly as the product of u and v and inversely as their sum. If x = 3 when u = 3 and v = 1, what is the value of x if u = 3 and v = 3?

Correct Answer: Option C

Explanation

(xpropto frac{uv}{u+v}\x = frac{kuv}{u+v}\K = frac{x(u+v)}{uv}\frac{3(3+1)}{3times1}\frac{3times4}{3}\k = 4\x=frac{4uv}{u+v}\x=frac{4times 3times3}{3+3}\x=frac{36}{6}\x=6)