I have two expressions:

(x/(2*sqrt(x+1)) + 1/(2*sqrt(x+1)*(sqrt(x+1)+1)))
((x*(sqrt(x+1)+1)+1)/(2*sqrt(x+1)*(sqrt(x+1)+1)))

As you see, they are identical, so full_simplify() method should
return the same result for both expressions. But:

sage: (x/(2*sqrt(x+1)) + 1/(2*sqrt(x+1)*(sqrt(x
+1)+1))).full_simplify()
1/2*(x + sqrt(x + 1))/(sqrt(x + 1) + 1)
sage: ((x*(sqrt(x+1)+1)+1)/(2*sqrt(x+1)*(sqrt(x
+1)+1))).full_simplify()
1/2*(sqrt(x + 1)*x + x + 1)/(x + sqrt(x + 1) + 1)

Although

sage: ((1/2*(x + sqrt(x + 1))/(sqrt(x + 1) + 1))/(1/2*(sqrt(x + 1)*x +
x + 1)/(x + sqrt(x + 1) + 1))).full_simplify()
1

Is this really a bug or I misunderstand something?

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