\(\dfrac{4}{\sqrt{5}-9}-\dfrac{4}{\sqrt{5}+2}=\dfrac{4\sqrt{5}+8-4\sqrt{5}+36}{\left(\sqrt{5}-9\right)\left(\sqrt{5}+2\right)}=\dfrac{44}{5+2\sqrt{5}-9\sqrt{5}-18}=\dfrac{-44}{7\sqrt{5}+13}\)

\(\sqrt{9-4\sqrt{5}}-\sqrt{5}\)

\(=\sqrt{\left(\sqrt{5}-2\right)^2}-\sqrt{5}\)

\(=\sqrt{5}-2-\sqrt{5}=-2\)

\(\dfrac{\sqrt{9-4\sqrt{5}}}{2-\sqrt{5}}=\dfrac{\sqrt{\left(\sqrt{5}-2\right)^2}}{2-\sqrt{5}}=\dfrac{\sqrt{5}-2}{2-\sqrt{5}}=\dfrac{-\left(2-\sqrt{5}\right)}{2-\sqrt{5}}=-1\)

\(\dfrac{\sqrt{9-4\sqrt{5}}}{2-\sqrt{5}}=-1\)

Ta có

A   =   5 ( x   +   4 ) 2   +   4 ( x   –   5 ) 2   –   9 ( 4   +   x ) ( x   –   4 )     =   5 ( x 2   +   2 . x . 4   +   16 )   +   4 ( x 2   –   2 . x . 5   +   5 2 )   –   9 ( x 2   –   4 2 )     =   5 ( x 2   +   8 x   +   16 )   +   4 ( x 2   –   10 x   +   25 )   –   9 ( x 2   –   4 2 )     =   5 x 2   +   40 x   +   80   +   4 x 2   –   40 x   +   100   –   9 x 2   +   144     = ( 5 x 2   +   4 x 2   –   9 x 2 )   +   ( 40 x   –   40 x )   +   ( 80   + 100   +   144 )

= 324

Đáp án cần chọn là: C

\(\sqrt{\dfrac{\left(4-\sqrt{5}\right)^2a^2}{9}}\)

\(=\dfrac{\sqrt{\left(4-\sqrt{5}\right)^2a^2}}{\sqrt{9}}\)

\(=\dfrac{\left|\left(4-\sqrt{5}\right)a\right|}{3}\)

\(=\dfrac{\left(4-\sqrt{5}\right)\left|a\right|}{3}\)

Quy đồng mẫu số: \(\frac{9}{11}=\frac{36}{44},\frac{5}{4}=\frac{55}{44}\).

Tử số ban đầu là \(36\)phần thì tử số mới là \(55\)phần.

Tử số ban đầu là: 

\(38\div\left(55-36\right)\times36=72\)

Mẫu số là: 

\(72\div9\times11=88\)

Phân số \(\frac{a}{b}=\frac{72}{88}\).

Tại sao tìm tử số lại có 2 lần số 36 nhỉ

1) \(\sqrt{9+4\sqrt{5}}-\sqrt{9-4\sqrt{5}}\)

\(=\sqrt{2^2+2\cdot2\cdot\sqrt{5}+\left(\sqrt{5}\right)^2}-\sqrt{2^2-2\cdot2\cdot\sqrt{5}+\left(\sqrt{5}\right)^2}\)

\(=\sqrt{\left(2+\sqrt{5}\right)^2}-\sqrt{\left(2-\sqrt{5}\right)^2}\)

\(=\left|2+\sqrt{5}\right|-\left|2-\sqrt{5}\right|\)

\(=2+\sqrt{5}+2-\sqrt{5}\)

\(=4\)

2) \(\sqrt{12-6\sqrt{3}}+\sqrt{12+6\sqrt{3}}\)

\(=\sqrt{3^2-2\cdot3\cdot\sqrt{3}+\left(\sqrt{3}\right)^2}+\sqrt{3^2+2\cdot3\cdot\sqrt{3}+\left(\sqrt{3}\right)^2}\)

\(=\sqrt{\left(3-\sqrt{3}\right)^2}+\sqrt{\left(3+\sqrt{3}\right)^2}\)

\(=\left|3-\sqrt{3}\right|+\left|3+\sqrt{3}\right|\)

\(=3-\sqrt{3}+3+\sqrt{3}\)

\(=6\)

\(\sqrt{9+4\sqrt{5}}-\sqrt{9-4\sqrt{5}}\)

\(=\sqrt{2^2+2.2.\sqrt{5}+\sqrt{5}^2}-\sqrt{2^2-2.2.\sqrt{5}+\sqrt{5}^2}\)

\(=\sqrt{\left(2+\sqrt{5}\right)^2}-\sqrt{\left(2-\sqrt{5}\right)^2}\)

\(=|2+\sqrt{5}|-|2-\sqrt{5}|\)

\(=2+\sqrt{5}-\sqrt{5}+2\)

\(=4\)