In the method of Integration using partial fraction method, the numerator is always kept to have 1 degree less than that of the denominator. Say, numerator would be Ax+B for a second degree denominator but just A for a linear denominator.
Why is it necessary to have a one degree one reference? I get that not having one degree less would cause problems when we solve the problem because we won't have all the variables to pair their coefficients, but I am seeking a more intuitive explanation.