\(ĐKXĐ:x\ne0\)

\(\frac{x+2}{x^2+2x+4}+\frac{x-2}{x^2-2x+4}=\frac{32}{x\left(x^4+4x^2+16\right)}\)

\(\Leftrightarrow\frac{x+2}{x^2+2x+4}+\frac{x-2}{x^2-2x+4}-\frac{32}{x\left(x^4+4x^2+16\right)}=0\)

\(\Leftrightarrow\frac{x\left(x+2\right)\left(x^2-2x+4\right)+x\left(x-2\right)\left(x^2+2x+4\right)-32}{x\left(x+2x+4\right)\left(x^2-2x+4\right)}=0\)

\(\Leftrightarrow x\left(x^3+8\right)+x\left(x^3-8\right)-32=0\)

\(\Leftrightarrow x\left(x^3+8+x^3-8\right)-32=0\)

\(\Leftrightarrow2x^4-32=0\)

\(\Leftrightarrow x^4=16\)

\(\Leftrightarrow x=\pm2\)

Vậy tập nghiệm của phương trình là \(S=\left\{2;-2\right\}\)

(5x+1)²=(3x+5)²

<=> (5x+1)²-(3x+5)²=0

<=> (5x+1+3x+5)(5x+1-3x-5)=0

<=> (8x+6)(2x-4)=0

\(\Leftrightarrow\orbr{\begin{cases}8x+6=0\\2x-4=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}8x=-6\\2x=4\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-\frac{3}{4}\\x=2\end{cases}}\)

Vậy......

\(\left(5x+1\right)^2=\left(3x+5\right)^2\)

\(\Leftrightarrow\orbr{\begin{cases}5x+1=3x+5\\5x+1=-3x-5\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}2x=4\\8x=-6\end{cases}}\)

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

\(ĐK:x\ne\frac{-2}{3};x\ne3\)

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

\(\Rightarrow\left(6x-1\right)\left(x-3\right)=\left(2x+5\right)\left(3x+2\right)\)

\(\Rightarrow6x^2-x-18x+3=6x^2+15x+4x+10\)

\(\Rightarrow-19x+3=19x+10\)

\(\Rightarrow38x=-7\Rightarrow x=\frac{-7}{38}\left(tm\right)\)

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

<=> (6x-1)(x-3)=(2x+5)(3x+2)

<=> 6x²-18x-x+3=6x²+4x+15x+10

<=> 6x²-19x+3=6x²+19x+10

<=> 6x²-19x-19x-6x²=10-3

<=> -38x=7

<=> x=-7/38

a) \(\frac{2a^2-3a-2}{a^2-4}=2\)

\(\Rightarrow2a^2-3a-2=2\left(a^2-4\right)\)

\(\Rightarrow2a^2-3a-2=2a^2-4\)

\(\Rightarrow-3a-2=-4\)

\(\Rightarrow-3a=-2\Rightarrow a=\frac{2}{3}\)

b) \(\frac{3a-1}{3a+1}+\frac{a-3}{a+3}=2\)

\(\Rightarrow\frac{\left(3a-1\right)\left(a+3\right)+\left(3a+1\right)\left(a-3\right)}{\left(3a+1\right)\left(a+3\right)}=2\)

\(\Rightarrow\frac{6a^2-6}{3a^2+10a+3}=2\)

\(\Rightarrow6a^2-6=2\left(3a^2+10a+3\right)\)

\(\Rightarrow6a^2-6=6a^2+20a+6\)

\(\Rightarrow-6=20a+6\Rightarrow20a=-12\)

\(\Rightarrow a=\frac{-3}{5}\)

a)\(x=\frac{43}{51}\)

b) \(x=\frac{1}{2},x=2\)

a) \(3-2x\left(25-2x\right)=4x^2+x-40\)

\(\Leftrightarrow3-50x+4x^2=4x^2+x-40\)

\(\Leftrightarrow51x-43=0\)

\(\Leftrightarrow x=\frac{43}{51}\)

Vậy tập nghiệm của phương trình là \(S=\left\{\frac{43}{51}\right\}\)

b) \(\left(x-2\right)\left(2x-3\right)=4-2x\)

\(\Leftrightarrow2x^2-7x+6=4-2x\)

\(\Leftrightarrow2x^2-5x+2=0\)

\(\Leftrightarrow2x^2-4x-x+2=0\)

\(\Leftrightarrow2x\left(x-2\right)-\left(x-2\right)=0\)

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

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

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

Vậy tập nghiệm của phương trình là \(S=\left\{\frac{1}{2};2\right\}\)

\(x^2\left(x^2+4\right)-x^2+4\)

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

\(=x^4+3x^2+4\)

\(=x^4-x^3+x^3+2x^2+2x^2-x^2-2x+2x+4\)

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

\(=x^2\left(x^2-x+2\right)+x\left(x^2-x+2\right)+2\left(x^2-x+2\right)\)

\(=\left(x^2+x+2\right)\left(x^2-x+2\right)\)