Question 1113598
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Easy way


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{{{A/x}}} + {{{B/(x+1)}}} = {{{(A*(x+1) + Bx)/(x*(x+1))}}} = {{{((A+B)x + A)/(x^2+x)}}}.


Since the right side is equal to  {{{(2x+1)/((x^2)+x)}}}, according to the condition, it implies for the coefficients

B = 1  and  A+B = 2.


Hence, B = 1 and A = 1.


<U>Answer</U>.  A = 1  and  B = 1.
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