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?

\(x\propto \frac{uv}{u+v}\)

x = \(\frac{kuv}{u+v}\)

K = \(\frac{x(u+v)}{uv}\)

\(\frac{3(3+1)}{3\times1}\)

\(\frac{3\times4}{3}\)

k = 4

x =\(\frac{4uv}{u+v}\)

x = \(\frac{4\times 3\times3}{3+3}\)

x = \(\frac{36}{6}\)

x = 6

There is an explanation video available below.

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