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a,\(2x\left(x-3\right)=x-3.\)

\(\Leftrightarrow2x=1\)

\(\Leftrightarrow x=\frac{1}{2}\)

Vậy ..... 

b, \(\frac{x+2}{x-2}-\frac{5}{x}=\frac{8}{x^2-2x}\)

\(\Leftrightarrow\frac{\left(x+2\right)\cdot x}{\left(x-2\right)\cdot x}-\frac{5\left(x-2\right)}{x\left(x-2\right)}=\frac{8}{x^2-2x}\)

\(\Leftrightarrow\frac{x^2+2x-\left(5x-10\right)}{\left(x-2\right)x}=\frac{8}{x^2-2x}\)

\(\Leftrightarrow\frac{x^2+2x-5x+10}{x^2-2x}=\frac{8}{x^2-2x}\)

\(\Leftrightarrow x^2+2x-5x+10=8\)

\(\Leftrightarrow x^2-3x+10-8=0\)

\(\Leftrightarrow x^2-x-2x+2=0\)

\(\Leftrightarrow x\left(x-1\right)-2\left(x-1\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(x-2\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x-1=0\\x-2=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=1\\x=2\end{cases}}}\)

Vậy ....

\(\frac{2x+1}{4}-\frac{x-5}{3}< \frac{4x-1}{12}+12.\)

\(\Leftrightarrow\frac{\left(2x+1\right)\cdot3}{4\cdot3}-\frac{\left(x-5\right)\cdot4}{3\cdot4}< \frac{4x-1}{12}+12.\)

\(\Leftrightarrow\frac{6x+3}{12}-\frac{4x-20}{12}< \frac{4x-1}{12}+12\)

\(\Leftrightarrow\frac{6x+3-4x+20}{12}< \frac{4x-1}{12}+12\)

\(\Leftrightarrow\frac{2x+23}{12}< \frac{4x-1}{12}+12\)

\(\Leftrightarrow\frac{2x+23-4x+1}{12}< 12\)

\(\Leftrightarrow\frac{-2x+24}{12}< 12\)

\(\Leftrightarrow-2x+24< 144\)

\(\Leftrightarrow-2x< 120\)

\(\Leftrightarrow x< -60\)

a) \(pt\Leftrightarrow\frac{6}{x^2+2}-1+\frac{7}{x^2+3}-1+\frac{12}{x^2+8}-1-\frac{3x^2+16}{x^2+10}+2=0\)

\(\Leftrightarrow\frac{4-x^2}{x^2+2}+\frac{4-x^2}{x^2+3}+\frac{4-x^2}{x^2+8}+\frac{4-x^2}{x^2+10}=0\)

\(\Leftrightarrow\left(4-x^2\right)\left(\frac{1}{x^2+2}+\frac{1}{x^2+3}+\frac{1}{x^2+8}+\frac{1}{x^2+10}\right)=0\)

\(\Leftrightarrow4-x^2=0\)(do \(\frac{1}{x^2+2}+\frac{1}{x^2+3}+\frac{1}{x^2+8}+\frac{1}{x^2+10}>0,\forall x\))

\(\Leftrightarrow x^2=4\Leftrightarrow x=\pm2\)

\(KL...\)

2x(8x - 1)²(4x - 1) = 9

<=> 512x⁴ - 256x³ + 40x² - 2x = 9

<=> 512x⁴ - 256x³ + 40x² - 2x - 9 = 0

<=> (2x - 1)(4x + 1)(64x⁴ - 16x + 9) = 0

vì 64x⁴ - 16x + 9 khác 0 nên:

<=> 2x - 1 = 0 hoặc 4x + 1 = 0

<=> x = 1/2 hoặc x = -1/4

Bài 1:

a, \(\frac{1}{x+1}+\frac{2}{x-1}=\frac{1+x^2}{x^2-1}\) (ĐKXĐ: x \(\ne\) \(\pm\) 1)

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

\(\Rightarrow\) x - 1 + 2(x + 1) = 1 + x²

\(\Leftrightarrow\) x - 1 + 2x + 2 - 1 - x² = 0

\(\Leftrightarrow\) -x² + 3x = 0

\(\Leftrightarrow\) x(3 - x) = 0

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\3-x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\left(TMĐKXĐ\right)\\x=3\left(TMĐKXĐ\right)\end{matrix}\right.\)

Vậy S = {0; 3}

b, \(\frac{x-2}{x+2}-\frac{x}{x-2}=\frac{8}{x^2-4}\) (ĐKXĐ: x \(\ne\) \(\pm\) 2)

\(\Leftrightarrow\) \(\frac{\left(x-2\right)^2}{\left(x+2\right)\left(x-2\right)}-\frac{x\left(x+2\right)}{\left(x+2\right)\left(x-2\right)}=\frac{8}{\left(x+2\right)\left(x-2\right)}\)

\(\Rightarrow\) (x - 2)² - x(x + 2) = 8

\(\Leftrightarrow\) (x - 2)² - x(x + 2) - 8 = 0

\(\Leftrightarrow\) x² - 4x + 4 - x² - 2x - 8 = 0

\(\Leftrightarrow\) -6x - 4 = 0

\(\Leftrightarrow\) x = \(\frac{-2}{3}\) (TMĐKXĐ)

Vậy S = {\(\frac{-2}{3}\)}

c, \(\frac{1}{x}\) + \(\frac{2}{x-3}\) = \(\frac{1-5x}{x^2-3x}\) (ĐKXĐ: x \(\ne\) 0; x \(\ne\) 3)

\(\Leftrightarrow\) \(\frac{x-3}{x\left(x-3\right)}+\frac{2x}{x\left(x-3\right)}=\frac{1-5x}{x\left(x-3\right)}\)

\(\Rightarrow\) x - 3 + 2x = 1 - 5x

\(\Leftrightarrow\) 3x - 3 = 1 - 5x

\(\Leftrightarrow\) 3x + 5x = 1 + 3

\(\Leftrightarrow\) 8x = 4

\(\Leftrightarrow\) x = \(\frac{1}{2}\) (TMĐKXĐ)

Vậy S = {\(\frac{1}{2}\)}

Bài 2:

a, \(\frac{1}{x+2}=\frac{5}{2-x}+\frac{12+x}{x^2-4}\)

\(\Leftrightarrow\) \(\frac{1}{x+2}=\frac{-5}{x-2}+\frac{12+x}{\left(x-2\right)\left(x+2\right)}\)

\(\Leftrightarrow\) \(\frac{x-2}{\left(x+2\right)\left(x-2\right)}=\frac{-5\left(x+2\right)}{\left(x+2\right)\left(x-2\right)}+\frac{12+x}{\left(x+2\right)\left(x-2\right)}\)

\(\Rightarrow\) x - 2 = -5(x + 2) + 12 + x

\(\Leftrightarrow\) x - 2 = -5x - 10 + 12 + x

\(\Leftrightarrow\) x - 2 = -4x + 2

\(\Leftrightarrow\) x + 4x = 2 + 2

\(\Leftrightarrow\) 5x = 4

\(\Leftrightarrow\) x = \(\frac{4}{5}\)

Vậy S = {\(\frac{4}{5}\)}

Chúc bn học tốt!! (Phần b hình như không có gì thì phải)

a) \(\frac{x+5}{4}-\frac{2x-3}{3}=\frac{6x-1}{8}+\frac{2x-1}{12}\)

<=> \(\frac{x}{4}+\frac{5}{4}-\frac{2x}{3}+1=\frac{6x}{8}-\frac{1}{8}+\frac{2x}{12}-\frac{1}{12}\)

<=> \(-\frac{4}{3}x=-\frac{59}{24}\)

<=> \(x=\frac{59}{32}\)

Vậy S = { 59/32}

b) \(\frac{\left(x+10\right)\left(x+4\right)}{12}-\frac{\left(x+4\right)\left(2-x\right)}{4}=\frac{\left(x+10\right)\left(x-2\right)}{3}\)

<=> \(\frac{x^2+14x+40}{12}-\frac{-x^2-2x+8}{4}=\frac{x^2+8x-20}{3}\)

<=> \(\left(\frac{x^2}{12}+\frac{x^2}{4}-\frac{x^2}{3}\right)+\left(\frac{14}{12}x+\frac{2}{4}x-\frac{8}{3}x\right)=-\frac{20}{8}+\frac{8}{4}-\frac{40}{12}\)

<=> \(-x=-8\)

<=> x = 8 

Vậy S = { 8 }

a/ Đặt \(x+\frac{1}{x}=a\Rightarrow x^2+\frac{1}{x^2}=a^2-2\)

\(\Leftrightarrow3\left(a^2-2\right)-16a+26=0\)

\(\Leftrightarrow3a^2-16a+20=0\Rightarrow\left[{}\begin{matrix}a=2\\a=\frac{10}{3}\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x+\frac{1}{x}=2\\x+\frac{1}{x}=\frac{10}{3}\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x^2-2x+1=0\\3x^2-10x+3=0\end{matrix}\right.\)

b/ \(\Leftrightarrow\left(x+2\right)\left(x+12\right)\left(x+3\right)\left(x+8\right)=4\)

\(\Leftrightarrow\left(x^2+14x+24\right)\left(x^2+11x+24\right)=4\)

Đề thiếu ko bạn? Vế phải là 4 hay \(4x^2\)?