((x+1)^(3/2)-x^(3/2))/x^(1/2)=((x+1)³-x³)/(x^(1/2)((x+1)^(3/2)+x^(3/2)))=(3x²+3x+1)/(x^(1/2)(x+1)^(3/2)+x^4)=(3x²+3x+1)/(x^(1/2)(x+1)^(3/2)+x²)=(3+3/x+1/x²)/(1+((x+1)/x)^(3/2))=3/(1+1)=3/2
