# Simplifying an answer returned by DSolveValue

Consider the IVP:

$$x'=\frac92-\frac{x}{300+2t},\quad x(0)=0$$

Working the solution by hand, the answer is:

$$x(t)=450+3t-\frac{4500\sqrt3}{\sqrt{300+2t}}$$

Entering code and then attempting to simplify, I tried Simplify and Expand.

In[214]:= sol =
DSolveValue[{x'[t] == 9/2 - x[t]/(300 + 2 t), x[0] == 0}, x[t], t]

Out[214]= -((
3 (750 Sqrt[6] - 150 Sqrt[150 + t] - t Sqrt[150 + t]))/Sqrt[150 + t])

In[215]:= Simplify[%]

Out[215]= 3 (150 - 750/Sqrt[25 + t/6] + t)

In[216]:= Expand[%]

Out[216]= 450 - 2250/Sqrt[25 + t/6] + 3 t


Is there a better way to simplify the answer so it looks more like my hand calculated answer, or if not, is there some way of getting clearing fractions from the radical in the denominator?

In this case, you can simply call Apart:
Apart[sol]

$$450+3 t-\frac{2250 \sqrt{6}}{\sqrt{t+150}}$$