Given that _ x ( 2+x^2 1+x -A x-B )=3 . What is the value of A?

Step-by-step solution

aligned & _ x ( 2+ x ^2 1+ x - Ax - B )=3 & _ x ( 2+ x ^2- Ax - B - Ax ^2- Bx 1+ x )=3 & _ x [ (1- A ) x ^2-( A + B ) x +2- B 1+ x ]=3 aligned Applying L'Hospital rule, 2 x(1-A)-(A+B)=3 Comparing coefficients array ll & 2(1-A)=0 & A=1 and & -(A+B)=3 & B=-3-1=-4 & A+B=-3 & A=1 . B=-4 array