Solve for k. a/b=b/a+1/k

k = ab / (a^2 - b^2)

Step-by-step explanation:

a/b=b/a+1/k

Multiply each side by abk to get rid of the fractions

abk * a/b=abk (b/a+1/k)

a^2k = b^2k + ab

Subtract b^2k from each side

a^2k - b^2k = b^2k - b^2k + ab

a^2 k - b^2 k = ab

Factor out k

k (a^2 - b^2) = ab

Divide each side by (a^2 - b^2)

k (a^2 - b^2) / (a^2 - b^2) = ab / (a^2 - b^2)

k = ab / (a^2 - b^2)