Simplify expression, skanavi 2.001 How can I simplify this expression?
$$
\frac {\sqrt{x}+1}{x\sqrt{x} + x +\sqrt{x}} \colon \frac {1}{x^2 - \sqrt{x}}
$$
Solving:
$$
a = \sqrt x
$$

$$
\frac {a+1}{a^3 + a^2 + a} \colon \frac{1}{a^4-a} = \frac{ a(a + 1)(a-1)(a^2 + a + 1) }{a(a^2 + a + 1)}  = (a +1)(a -1)=a^2-1 
$$
Anser is: $x - 1$

Notice that $x^2 - \sqrt{x} = \sqrt{x}\Big( (\sqrt{x})^3 - 1 \Big)$ and use the formula $a^3 - 1 = (a -1)(a^2+a+1)$
