Maths Edexcel C1 "Simplifying sums and differences of fractional powers"

I'm trying to understand the example in the photo which is from page 8 of "Modular Maths for Edexcel 2nd Edition Core Maths 1 & 2" - Sykes.




I get Example 1.6 but 1.7 baffles me.

From the first line of the solution starting "The expression is ...", If I take out the trailing

(x + 7)^1/2

I can't see how
3(x + 7)^1/2 - 2/3(x + 7)

can become

{3 - 2/3(x - 7)} (x+7)^1/2

Well, there is a common factor and also note that (x+7)^3/2=(x+7)times (x+7)^1/2 and so (x+7)^1/2 can also be a common factor.

Edit, there is also typo which does not help where (x-7) is written instead of (x+7) in line 3