a) Điều kiện xác định: \(a > 0\); \(a \neq 1\) và \(a \neq 2\).

\(P = \left(\right. \frac{1}{\sqrt{a} - 1} - \frac{1}{\sqrt{a}} \left.\right) : \left(\right. \frac{\sqrt{a} + 1}{\sqrt{a} - 2} - \frac{\sqrt{a} + 2}{\sqrt{a} - 1} \left.\right)\)

\(= \frac{\sqrt{a} - \sqrt{a} + 1}{\left(\right. \sqrt{a} - 1 \left.\right) \sqrt{a}} : \left[\right. \frac{\left(\right. \sqrt{a} + 1 \left.\right) \left(\right. \sqrt{a} - 1 \left.\right)}{\left(\right. \sqrt{a} - 1 \left.\right) \left(\right. \sqrt{a} - 2 \left.\right)} - \frac{\left(\right. \sqrt{a} + 2 \left.\right) \left(\right. \sqrt{a} - 2 \left.\right)}{\left(\right. \sqrt{a} - 1 \left.\right) \left(\right. \sqrt{a} - 2 \left.\right)} \left]\right.\)

\(= \frac{1}{\left(\right. \sqrt{a} - 1 \left.\right) \sqrt{a}} : \frac{a - 1 - a + 4}{\left(\right. \sqrt{a} - 1 \left.\right) \left(\right. \sqrt{a} - 2 \left.\right)}\)

\(= \frac{1}{\left(\right. \sqrt{a} - 1 \left.\right) \sqrt{a}} . \frac{\left(\right. \sqrt{a} - 1 \left.\right) \left(\right. \sqrt{a} - 2 \left.\right)}{3}\)

\(= \frac{\sqrt{a} - 2}{3 \sqrt{a}}\)

b) Để \(P > \frac{1}{6}\) thì \(\frac{\sqrt{a} - 2}{3 \sqrt{a}} > \frac{1}{6}\).

Vì \(\sqrt{a} > 0\) thỏa mãn điều kiện xác định nên để \(\frac{\sqrt{a} - 4}{6 \sqrt{a}} > 0\) thì \(\sqrt{a} - 4 > 0.\)

\(\sqrt{a} > 4\)

\(a > 16\).

thay x=9 vào biểu thức A ta được

A=3 căn 9 phần căn 9 +2

= 9 phần 5

B=B=(x​+2)(x​−2)x+4​−x​−22​

\(= \frac{x + 4 - 2 \left(\right. \sqrt{x} + 2 \left.\right)}{\left(\right. \sqrt{x} + 2 \left.\right) \left(\right. \sqrt{x} - 2 \left.\right)}\)

\(= \frac{x - 2 \sqrt{x}}{\left(\right. \sqrt{x} + 2 \left.\right) \left(\right. \sqrt{x} - 2 \left.\right)}\)

\(= \frac{\sqrt{x} \left(\right. \sqrt{x} - 2 \left.\right)}{\left(\right. \sqrt{x} + 2 \left.\right) \left(\right. \sqrt{x} - 2 \left.\right)}\)

\(= \frac{\sqrt{x}}{\sqrt{x} + 2}\)

 \(A - B = \frac{2 \sqrt{x}}{\sqrt{x} + 2}\)

\(A - B < \frac{3}{2}\) khi \(\frac{2 \sqrt{x}}{\sqrt{x} + 2} < \frac{3}{2}\)

\(4 \sqrt{x} < 3 \sqrt{x} + 6\) vì \(x \geq 0\) nên \(\sqrt{x} + 2 > 0\)

\(\sqrt{x} < 6\)

\(x < 36\)

Sometimes living in the city can be a bit frustrating. First, traffic jams are a big problem. It can take a long time to get anywhere by bus because of all the cars on the road. Second, everything seems expensive in the city. From groceries to movie tickets, prices are higher than in smaller towns. Overall, the city can be a great place, but it's not perfect.