What fraction of the form Ax+3 can be added to 6xx2+2x−3 so that the result reduces to a fraction of the form Bx−1? Here A and B are real numbers. Give the value of A as your answer.
Ax+3+6xx2+2x−3=Bx−1Ax+3+6x(x+3)(x−1)=Bx−1A(x−1)+6x(x+3)(x−1)=B(x+3)(x+3)(x−1)
(A+6)x−A=Bx+3B
A+6=B−A=3BSolve these two equations for A,B
