Question

f(x) 2? + 20 can be written in the form of 23 + 2.2 The partial fraction decomposition of where + 9(2) 22 h(2) 2+2' I f(2)= g(x) = h(2)

Answer 1

x220 3+ 2x2 2+20 22(x+2) Partial traction decomposition, now A B. 4 + C 772. x+20 x(x+2) ne a A (x+2)X + B(at2) & car x²(xt) र) 22 +20 An(n+2) + B (at2) + Ca ut 0 78 o+ B(ote) to - 2B 8=10 put = -2. 4+20 0 + 0 + 46 24 - 46 IC=C

now Compare the coff. of xl = A + c A = 1-c Put value of a A = 1-6 A=-5 no lo x² +20 x²(x+2) + q २ Hence f(x) = -5 190)= to hu) = 6