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

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!