If 17 x-2 12 x^2-x-20 = A a x+5 + B 3 x+b then a A+b B=

Step-by-step solution

Given 17 x-2 12 x^2-x-20 = A (a x+5) + B 3 x+b ...(i) Now 17 x-2 12 x^2-x-20 = 17 x-2 (3 x-4)(4 x+5) By using partial fraction, RHS can be written as: aligned & 17 x-2 12 x^2-x-20 = P (3 x-4) + Q 4 x+5 ...(ii) & 17 x-2=P(4 x+5)+Q(3 x-4)=x(4 P+3 Q)+(5 P-4 Q) aligned From above equation, we get: P=2, Q=3 Putting above values in equation (ii), we get: 17 x-2 12 x^2-x-20 = 2 (3 x-4) + 3 4 x+5 ...(iii) Comparing eqn (i) & (iii), we get aligned & A=2, B=3, a=-4, b=4 & a A+b B=-4.2+(4) 3=4 aligned