Giải thích các bước giải:
$ĐK : a > 0 ; a \neq 1$
$1, P = (\frac{√a + 1}{√a - 1} - \frac{√a - 1}{√a + 1} + 4√a).\frac{1}{2a√a}$
$P = \frac{(√a + 1)² - (√a - 1)² + 4√a(√a + 1)(√a - 1)}{(√a - 1)(√a + 1)} . \frac{1}{2a√a}$
$P= \frac{a + 2√a + 1 - (a -2√a + 1) + 4√a(a - 1)}{a - 1} . \frac{1}{2a√a}$
$P = \frac{a + 2√a + 1 - a + 2√a - 1 + 4a√a - 4√a}{a-1}. \frac{1}{2a√a}$
$P = \frac{4a√a}{a - 1}.\frac{1}{2a√a}$
$P = \frac{2}{a - 1}$
$2, P = a$
$→\frac{2}{a - 1} = a$
$→ a(a - 1) = 2$
$→ a² - a - 2 = 0$
$→ (a² - 2a) + (a - 2) = 0$
$→ a(a - 2) + (a - 2) = 0$
$→ (a + 1)(a - 2)=0$
$→\left[ \begin{array}{l}a + 1 = 0\\a - 2 = 0\end{array} \right.→\left[ \begin{array}{l}x=-1(tmđk)\\x=2(tmđk)\end{array} \right.$