a)\(\left(x^2+1\right)\left(x^2-4x+4\right)=0\Leftrightarrow\orbr{\begin{cases}x^2+1=0\\x^2-4x+4=0\end{cases}\Rightarrow\orbr{\begin{cases}x^2=-1\left(vn\right)\\\left(x-2\right)^2=0\end{cases}\Rightarrow}x=2}\)

b)\(\left(3x-2\right)\left(\frac{2x+6}{7}-\frac{4x-3}{5}\right)=0\\ \Rightarrow\left(3x-2\right)\left(\frac{10x+30-28x+21}{35}\right)=0\)

\(\Rightarrow\left(3x-2\right)\left(\frac{-18x+51}{35}\right)=0\Rightarrow\orbr{\begin{cases}x=\frac{2}{3}\\x=\frac{17}{6}\end{cases}}\)

c)\(\left(3,3-11x\right)\left(\frac{21x+6+10-30x}{15}\right)=0\Leftrightarrow\orbr{\begin{cases}x=\frac{3}{10}\\x=\frac{16}{9}\end{cases}}\)

a) \(\left(3x-2\right)\left(\frac{10x\left(x+3\right)-7\left(4x-3\right)}{35}\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}3x-2=0\\-18x+51=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\frac{2}{3}\\x=\frac{17}{6}\end{matrix}\right.\)

b)\(\left(3,3x-11\right)\left(\frac{3\left(7x+2\right)+10\left(1-3x\right)}{15}\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\frac{3}{10}\\x=\frac{16}{9}\end{matrix}\right.\)

\(\frac{5x-3}{6}-\frac{7x-1}{4}-\frac{4x+2}{7}+5=0\)

<=> \(\frac{14\left(5x-3\right)-21\left(7x-1\right)-12\left(4x+2\right)+420}{84}=0\)

<=> 70x - 42 - 147x + 21 - 48x -24 + 420 = 0

<=> -125x + 375 = 0

<=> -125x = -375

<=> x = 3

Vậy S = {3}

\(\frac{3\left(2x+1\right)}{4}-5-\frac{3x+2}{10}=\frac{2\left(3x-1\right)}{5}\)

<=> \(\frac{15\left(2x+1\right)-100-2\left(3x+2\right)}{20}=\frac{8\left(3x-1\right)}{20}\)

<=> 30x + 15 - 100 - 6x - 4 = 24x - 8

<=> 24x - 24x = -8 + 89

<=> 0x = 81

=> pt vô nghiệm

a) \(\left(4x-10\right)\left(24+5x\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}4x-10=0\\24+5x=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{10}{4}=\dfrac{5}{2}\\x=-\dfrac{24}{5}\end{matrix}\right.\)

Vậy \(S=\left\{-\dfrac{24}{5};\dfrac{5}{2}\right\}\)

b) \(\left(3.5-7x\right)\left(0.1x+2.3\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}3.5-7x=0\\0.1x+2.3=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{3.5}{7}=\dfrac{1}{2}\\x=-\dfrac{2.3}{0.1}=-23\end{matrix}\right.\)

Vậy \(S=\left\{-23;\dfrac{1}{2}\right\}\)

\(\left(3x-2\right)\left(4x+5\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}3x-2=0\\4x+5=0\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=\frac{2}{3}\\x=-\frac{5}{4}\end{cases}}\)

ĐKXĐ: x khác -4;-5;-6;-7

\(\frac{1}{x^2+9x+20}+\frac{1}{x^2+11x+30}+\frac{1}{x^2+13x+42}=\frac{1}{18}\)

\(\Rightarrow\frac{1}{\left(x+4\right).\left(x+5\right)}+\frac{1}{\left(x+5\right).\left(x+6\right)}+\frac{1}{\left(x+6\right).\left(x+7\right)}=\frac{1}{18}\)

\(\Rightarrow\frac{1}{x+4}-\frac{1}{x+5}+\frac{1}{x+5}-\frac{1}{x+6}+\frac{1}{x+6}-\frac{1}{x+7}=\frac{1}{18}\)

\(\Rightarrow\frac{1}{x+4}-\frac{1}{x+7}=\frac{1}{18}\)

\(\Rightarrow\frac{x+7-x-4}{\left(x+4\right).\left(x+7\right)}=\frac{1}{18}\Rightarrow3.18=x^2+11x+28\)

\(\Rightarrow x^2+11x-26=0\)

\(\Rightarrow\left(x-2\right).\left(x+13\right)=0\)

\(\Rightarrow\orbr{\begin{cases}x=2\\x=-13\end{cases}\left(tm\right)}\)

Vậy...

a) Ta có: \(\frac{2\left(x-4\right)}{3}+\frac{3x+13}{8}=\frac{2\left(2x-3\right)}{5}+12\)

⇔\(\frac{80\left(x-4\right)}{120}+\frac{15\left(3x+13\right)}{120}-\frac{48\left(2x-3\right)}{120}-\frac{1440}{120}=0\)

⇔\(80\left(x-4\right)+15\left(3x+13\right)-48\left(2x-3\right)-1440=0\)

\(\Leftrightarrow80x-320+45x+195-96x+144-1440=0\)

⇔\(29x-1421=0\)

\(\Leftrightarrow29x=1421\)

hay x=49

Vậy: x=49

b) Ta có: \(\frac{2\left(5x+2\right)}{9}-1=\frac{4\left(33+2x\right)}{5}-\frac{5\left(1-11x\right)}{9}\)

⇔\(\frac{10\left(5x+2\right)}{45}-\frac{45}{45}-\frac{36\left(33+2x\right)}{45}+\frac{25\left(1-11x\right)}{45}=0\)

⇔\(10\left(5x+2\right)-45-36\left(33+2x\right)+25\left(1-11x\right)=0\)

\(\Leftrightarrow50x+20-45-1188-72x+25-275x=0\)

\(\Leftrightarrow-297x-1188=0\)

\(\Leftrightarrow-297x=1188\)

hay x=-4

Vậy: x=-4