Simplify expression, skanavi 2.001

Question

How can I simplify this expression?

$$ \frac {\sqrt{x}+1}{x\sqrt{x} + x +\sqrt{x}} \colon \frac {1}{x^2 - \sqrt{x}} $$

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

@ozik.dev, did you get Yuri's hint? – Vikram May 30 '14 at 08:41 — Vikram, May 30 '14 at 08:41
@Vikram, yes thanks, i try to understand his answer :) – ozik.dev May 30 '14 at 08:43 — ozik.dev, May 30 '14 at 08:43
$a^2 = x$ because a = $\sqrt x$ – ozik.dev May 30 '14 at 09:11 — ozik.dev, May 30 '14 at 09:11
$\frac{a}{b}:\frac{c}{d}$ implies $ad=bc$ – Vikram May 30 '14 at 09:13 — Vikram, May 30 '14 at 09:13

score 3 · Accepted Answer · answered May 30 '14 at 08:33

3

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

answered May 30 '14 at 08:33

Yuri Vyatkin

1 Answers1