26 ,giải phương trình.
a,\(\frac{1}{x-1}+\frac{2}{x^2+x+1}=\frac{3x^2}{x^3-1}\)
b,\(\frac{x}{2\left(x-3\right)}+\frac{x}{2\left(x+1\right)}=\frac{2x}{\left(x+1\right)\left(x-3\right)}\)
c,\(\frac{x-1}{x+2}+\frac{x-2}{x+1}=\frac{2\left(x^2+2\right)}{x^2-4}\)
d,\(\frac{3}{5x-1}+\frac{2}{3-5x}=\frac{4}{\left(1-5x\right)\left(x-3\right)}\)
\(\frac{x\left(x+1\right)}{2\left(x+1\right)\left(x-3\right)}+\frac{x\left(x-3\right)}{2\left(x+1\right)\left(x-3\right)}=\frac{4x}{2\left(x+1\right)\left(x-3\right)}\)
\(\Leftrightarrow x^2+x+x^2-3x=4x\Leftrightarrow2x^2-6x=0\Leftrightarrow2x\left(x-3\right)=0\Rightarrow\left[{}\begin{matrix}x=0\\x=3\end{matrix}\right.\)
\(\Leftrightarrow\frac{x^2+x+1}{x^3-1}+\frac{2\left(x-1\right)}{x^3-1}=\frac{3x^2}{x^3-1}\)
\(\Leftrightarrow x^2+x+1+2x-2=3x^2\Leftrightarrow2x^2-3x+1=0\Leftrightarrow2x^2-2x-x+1=0\Leftrightarrow2x\left(x-1\right)-\left(x-1\right)=0\Leftrightarrow\left(2x-1\right)\left(x-1\right)=0\Rightarrow\left[{}\begin{matrix}x=\frac{1}{2}\\x=1\end{matrix}\right.\)
