Bài 1: 

b: \(\Leftrightarrow x-2=0\)

hay x=2

a:Sửa đề: \(\dfrac{3}{5x-1}+\dfrac{2}{3-x}=\dfrac{4}{\left(1-5x\right)\left(x-3\right)}\)

=>3x-9-10x+2=-4

=>-7x-7=-4

=>-7x=3

=>x=-3/7

b: =>\(\dfrac{5-x}{4x\left(x-2\right)}+\dfrac{7}{8x}=\dfrac{x-1}{2x\left(x-2\right)}+\dfrac{1}{8\left(x-2\right)}\)

=>\(2\left(5-x\right)+7\left(x-2\right)=4\left(x-1\right)+x\)

=>10-2x+7x-14=4x-4+x

=>5x-4=5x-4

=>0x=0(luôn đúng)

Vậy: S=R\{0;2}

\(1,\) thiếu đề

\(2,\dfrac{5x+2}{6}-\dfrac{8x-1}{3}=\dfrac{4x+2}{5}-5\)

\(\Leftrightarrow\dfrac{5\left(5x+2\right)}{30}-\dfrac{10\left(8x-1\right)}{30}=\dfrac{6\left(4x+2\right)}{30}-\dfrac{150}{30}\)

\(\Leftrightarrow5\left(5x+2\right)-10\left(8x-1\right)=6\left(4x+2\right)-150\)

\(\Leftrightarrow25x+10-80x+10=24x+12-150\)

\(\Leftrightarrow-55x+20=24x-138\)

\(\Leftrightarrow24x-138+55x-20=0\)

\(\Leftrightarrow79x-158=0\)

\(\Leftrightarrow x=2\)

\(3,ĐKXĐ:\left\{{}\begin{matrix}x\ne1\\x\ne-1\\x\ne3\end{matrix}\right.\\ \dfrac{x}{2x-6}+\dfrac{x}{2x-2}=\dfrac{-2x}{\left(x+1\right)\left(3-x\right)}\)

\(\Leftrightarrow\dfrac{x}{2\left(x-3\right)}+\dfrac{x}{2\left(x-1\right)}+\dfrac{2x}{\left(x+1\right)\left(3-x\right)}=0\)

\(\Leftrightarrow\dfrac{x}{2\left(x-3\right)}+\dfrac{x}{2\left(x-1\right)}-\dfrac{2x}{\left(x+1\right)\left(x-3\right)}=0\)

\(\Leftrightarrow x\left(\dfrac{1}{2\left(x-3\right)}+\dfrac{1}{2\left(x-1\right)}-\dfrac{2}{\left(x+1\right)\left(x-3\right)}\right)=0\)

\(\Leftrightarrow x\left(\dfrac{\left(x-1\right)\left(x+1\right)}{2\left(x-1\right)\left(x-3\right)\left(x+1\right)}+\dfrac{\left(x-3\right)\left(x+1\right)}{2\left(x-1\right)\left(x-3\right)\left(x+1\right)}-\dfrac{4\left(x-1\right)}{2\left(x+1\right)\left(x-3\right)\left(x-1\right)}\right)=0\)

\(\Leftrightarrow x\left(\dfrac{x^2-1}{2\left(x-1\right)\left(x-3\right)\left(x+1\right)}+\dfrac{x^2-2x-3}{2\left(x-1\right)\left(x-3\right)\left(x+1\right)}-\dfrac{4x-4}{2\left(x+1\right)\left(x-3\right)\left(x-1\right)}\right)=0\)

\(\Leftrightarrow x.\dfrac{x^2-1+x^2-2x-3-4x+4}{2\left(x-1\right)\left(x-3\right)\left(x+1\right)}=0\)

\(\Leftrightarrow x.\dfrac{2x^2-6x}{2\left(x-1\right)\left(x-3\right)\left(x+1\right)}=0\)

\(\Leftrightarrow x.\dfrac{2x\left(x-3\right)}{2\left(x-1\right)\left(x-3\right)\left(x+1\right)}=0\)

\(\Leftrightarrow x.\dfrac{x}{\left(x-1\right)\left(x+1\right)}=0\)

\(\Leftrightarrow\dfrac{x^2}{\left(x-1\right)\left(x+1\right)}=0\)

\(\Leftrightarrow x=0\)

Câu a:

\(2x\left(8x-1\right)^2\left(4x-1\right)=9\)

\(\Leftrightarrow\left(64x^2-16x+1\right)\left(64x^2-16x\right)=72\)

Đặt 64x² - 16x = t \(\left(t\ge-1\right)\)

\(\Rightarrow t\left(t+1\right)=72\)

\(\Leftrightarrow\left(t+9\right)\left(t-8\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}t=-9\left(loai\right)\\t=8\left(nhan\right)\end{matrix}\right.\)

\(\Rightarrow64x^2-16x=8\)

\(\Leftrightarrow8\left(2x-1\right)\left(4x+1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\x=-\dfrac{1}{4}\end{matrix}\right.\)

Câu b:

\(\Leftrightarrow\left(x+1\right)^2\left(2x+1\right)\left(2x+3\right)=18\)

\(\Leftrightarrow\left(4x^2+8x+4\right)\left(4x^2+8x+3\right)=72\)

Đặt 4x² + 8x + 4 = m \(\left(m\ge0\right)\)

\(\Rightarrow m\left(m-1\right)=72\)

\(\Leftrightarrow\left(m-9\right)\left(m+8\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}m=9\left(nhan\right)\\m=-8\left(loai\right)\end{matrix}\right.\)

\(\Rightarrow4\left(x+1\right)^2=9\)

\(\Leftrightarrow x+1=\pm\dfrac{3}{2}\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{5}{2}\\x=\dfrac{1}{2}\end{matrix}\right.\)

\(\Rightarrow2x\cdot\left(64x^2-16x+1\right)\cdot\left(4x-1\right)=9\)

\(\Rightarrow\left(64x^2-16x+1\right)\cdot\left(8x^2-2x\right)=9\)

Nhân cả hai vế của phương trình với 8 ta được:

\(\left(64x^2-16x+1\right)\cdot\left(64x^2-16x\right)=72\)

Đặt \(a=64x^2-16x\left(a\ge1\right)\) (1)

\(\Rightarrow\left(a+1\right)\cdot a=72\)

\(\Rightarrow a^2+a-72=0\)

\(\Rightarrow\left(a-8\right)\cdot\left(a+9\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}a=8\left(tmđk\right)\\a=-9\left(loại\right)\end{matrix}\right.\)

Thay vào (1) ta đc:

\(64x^2-16x=8\Rightarrow64x^2-16x-8=0\)

\(\Rightarrow\left(2x-1\right)\left(4x+1\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\x=-\dfrac{1}{4}\end{matrix}\right.\)

$2x{}^{}\left(4x-1\right)=9$

$\iff \left(64{}^{}-16x+1\right)\left(64{}^{}-16x\right)=72$

Đặt 64x2 - 16x = t $\left(t\ge -1\right)$

$\Rightarrow t\left(t+1\right)=72$

$\iff \left(t+9\right)\left(t-8\right)=0$

⇔[ t=−9
t=8
⇔[t=−9(loai)t=8(nhan

$\Rightarrow 64{}^{}-16$