Answer
$\frac{1}{2}(x+1)^{1/2}(5x+2)=\frac{1}{2}\sqrt{x+1}(5x+2)$
Work Step by Step
We simplify:
$(x+1)^{3/2}+x\displaystyle *\frac{3}{2}(x+1)^{1/2}
=(x+1)^{1/2}((x+1)^{2/2}+\frac{3}{2}x)=(x+1)^{1/2}(x+1+\frac{3}{2}x)=(x+1)^{1/2}(\frac{5}{2}x+1)=(x+1)^{1/2}(\frac{5}{2}x+\frac{2}{2})=\frac{1}{2}(x+1)^{1/2}(5x+2)=\frac{1}{2}\sqrt{x+1}(5x+2)$
