\(\dfrac{12808125}{16}\)

Lần sau ghi dấu ra xíu nhé :v

a) Đặt \(\sqrt{x}=a\Rightarrow B=\left(\dfrac{a}{a+4}+\dfrac{4}{a-4}\right):\dfrac{a^2+16}{a+2}\)

Quy đồng,rút gọn : \(B=\dfrac{a+2}{a^2-16}\Rightarrow B=\dfrac{\sqrt{x}+2}{x-16}\)

b) \(B\left(A-1\right)=\dfrac{\sqrt{x}+2}{x-16}\left(\dfrac{\sqrt{x}+4}{\sqrt{x}+2}-1\right)=\dfrac{2}{x-16}\)

x - 16 là ước của 2 => \(x\in\left\{14;15;17;18\right\}\)

mới làm quen toán 9 ;v có gì k rõ ae chỉ bảo nhé :))

\(A=\dfrac{-\left(\sqrt{x}+1\right)\left(2+\sqrt{x}\right)-2\sqrt{x}\left(2-\sqrt{x}\right)+5\sqrt{x}+2}{\left(2+\sqrt{x}\right)\left(2-\sqrt{x}\right)}:\dfrac{\sqrt{x}\left(3-\sqrt{x}\right)}{\left(\sqrt{x}+2\right)^2}\)

\(A=\dfrac{-3\sqrt{x}-x-2-4\sqrt{x}+2x+5\sqrt{x}+2}{\left(2+\sqrt{x}\right)\left(2-\sqrt{x}\right)}.\dfrac{\left(\sqrt{x}+2\right)^2}{\sqrt{x}\left(3-\sqrt{x}\right)}\)

\(A=\dfrac{-x-2\sqrt{x}}{\left(2+\sqrt{x}\right)\left(2-\sqrt{x}\right)}.\dfrac{\left(\sqrt{x}+2\right)^2}{\sqrt{x}\left(3-\sqrt{x}\right)}\)

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

CHÚC BẠN HỌC TỐT NHÉ

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

        \(M=1.\left(a+b\right)\left(a^2+b^2\right).......\)

    \(=\left(a-b\right)\left(a+b\right)\left(a^2+b^2\right)....\)

   \(=\left(a^2-b^2\right)\left(a^2+b^2\right)....\)

                        \(=\left(a^4-b^4\right)\left(a^4+b^4\right)......\)

                                            \(=\left(a^8-b^8\right)\left(a^8+b^8\right)\left(a^{16}+b^{16}\right)\)

                                                             \(=\left(a^{16}-b^{16}\right)\left(a^{16}+b^{16}\right)\)

                                                              \(=a^{32}-b^{32}\)

\(B=\left(\dfrac{\sqrt{x}}{\sqrt{x}-2}-\dfrac{2}{\sqrt{x}+2}\right):\dfrac{x+4}{\sqrt{x}+2}\left(dkxd:x\ne4\right)\)

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

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

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

\(=\dfrac{1}{\sqrt{x}-2}\)

Vậy \(B=\dfrac{1}{\sqrt{x}-2}\)

Ta có:

\(A=\left(x-4\right)\left(x-2\right)-\left(x-1\right)\left(x-3\right)\)

\(A=\left(x^2-4x-2x+8\right)-\left(x^2-x-3x+4\right)\)

\(A=\left(x^2-6x+8\right)-\left(x^2-4x+4\right)\)

\(A=x^2-6x+8-x^2+4x-4\)

\(A=-2x+4\)

Thay \(x=1\dfrac{3}{4}=\dfrac{7}{4}\) vào A ta được:

\(A=-2.\dfrac{7}{4}+4\)

\(A=-\dfrac{7}{2}+4\)

\(A=\dfrac{1}{2}\)

\(\dfrac{-8^3\cdot6^4}{18^{12}}=\dfrac{2^3\cdot4^3\cdot2^2\cdot3^2}{2^{12}\cdot3^{12}\cdot3^{12}}\)

\(=\dfrac{2^5\cdot\left(2^2\right)^3\cdot3^2}{2^{12}\cdot3^{12}\cdot3^{12}}=\dfrac{2^6}{2^7\cdot3^{10}\cdot3^{12}}\)

\(=\dfrac{1}{2\cdot3^{22}}\)