\(\dfrac{\left(-1\right)^6.3^5.4^3}{9^3.2^5}=\dfrac{1.3^5.\left(2^2\right)^3}{\left(3^2\right)^3.2^5}=\dfrac{1.3^5.2^6}{3^6.2^5}=\dfrac{2}{3}\)

\(\dfrac{\left(-1\right)^6.3^5.4^3}{9^3.2^5}=\dfrac{1.3^5.2^6}{3^6.2^5}=\dfrac{2}{3}\)

3n-6 không bằng 3(n-3) bạn nha

\(\dfrac{3n+2}{n-3}=\dfrac{3\left(n-3\right)}{n-3}+\dfrac{8}{n-3}=3+\dfrac{8}{n-3}\)

Để \(\dfrac{3n+2}{n-3}\in Z\) thì \(\left(n-3\right)\inƯ\left(8\right)=\left\{1;-1;2;-2;4;-4;8;-8\right\}\)

Vì \(n\in N\Rightarrow n\in\left\{4;2;5;1;7;11\right\}\)

\(3x-\sqrt{x^2-2x+1}\left(1\right)=3x-\sqrt{\left(x-1\right)^2}=3x-\left|x-1\right|\)

TH1: x<1

\(\left(1\right)=3x+x-1=4x-1\)

TH2: \(x\ge1\)

\(\left(1\right)=3x-x+1=2x+1\)

\(\sqrt{x+9}=5-\sqrt{2x+4}\left(đk:4\ge x\ge-2\right)\Leftrightarrow\sqrt{x+9}+\sqrt{2x+4}=5\Leftrightarrow x+9+2x+4+2\sqrt{\left(x+9\right)\left(2x+4\right)}=25\Leftrightarrow12-3x=2\sqrt{\left(x+9\right)\left(2x+4\right)}\Leftrightarrow144-72x+9x^2=4\left(2x^2+22x+36\right)\Leftrightarrow x^2-160x=0\Leftrightarrow x\left(x-160\right)=0\)\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=160\end{matrix}\right.\)(0 thỏa đk, 160 không thỏa)\(\Leftrightarrow x=0\)

\(x-4+\sqrt{x^2-8x+16}\left(1\right)=x-4+\sqrt{\left(x-4\right)^2}=x-4+\left|x-4\right|\)

TH1: x<4

\(\left(1\right)=x-4-x+4=0\)

TH2: \(x\ge4\)

\(\left(1\right)=x-4+x-4=2x-8\)

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

a) \(\left(x+2\right)\left(2x-4\right)-\left(2x+1\right)^2=2\left(x^2-4\right)-\left(2x+1\right)^2=2x^2-8-4x^2-4x-1=-2x^2-4x-9=-2\left(-\dfrac{1}{5}\right)^2-4.\dfrac{-1}{5}-9=-\dfrac{207}{25}\)b) \(B=\left(2x+1\right)^2-\left(x-1\right)^2=4x^2+4x+1-x^2+2x-1=3x^2+6x=2.\left(\dfrac{1}{6}\right)^2+6.\dfrac{1}{6}=\dfrac{19}{18}\)c) \(C=\left(x-y\right)^2+2\left(x^2-y^2\right)+\left(x+y\right)^2=\left(x-y+x+y\right)^2=4x^2=4.\left(0,75\right)^2=\dfrac{9}{4}\)

Tử số là: \(\left(51-19\right):2=16\)

Mẫu số là: \(\left(51+19\right):2=35\)

Vậy phân số đó là: \(\dfrac{16}{35}\)