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Problem set on job finding, job separation and the equilibrium unemployment rate

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Problem set on job finding, job separation and the equilibrium unemployment rate. As in the model presented in class, U is the total number of unemployed people. E is the total number of employed people. The labor force L = U + E. The number of people in the labor force is fixed. The unemployment rate is u = U /L. The number of people losing jobs in a period is sE where s is a fraction (between zero and one). Unlike the model presented in class, the number of unemployed people finding jobs in a period is fU - gE where f and g are both fractions (between zero and one). Derive the long-run equilibrium value of the unemployment rate u. Show your work!