rút gọn phân thức
1)\(\frac{x}{x-3}-\frac{x^2+3x}{2x+3}.\left(\frac{x+3}{x^2-3x}-\frac{x}{x^2-9}\right)\)
2)\(\frac{x^2-6}{x-3}+\frac{x^2+3}{2x+3}.\left(\frac{x}{x^2-9}-\frac{x+3}{x^2-3x}\right)\)
3)\(\left(\frac{x}{x^2-36}-x-\frac{6}{x^2+6x}\right)\colon\frac{2x-6}{x^2+6x}+\frac{x}{6-x}\)

1)ĐKXĐ: x≠3 ; x≠0 x≠\(-3;x\ne-\frac32\)
\(\frac{x}{x-3}-\frac{x^2+3x}{2x+3}\cdot\left(\frac{x+3}{x^2-3x}-\frac{x}{x^2-9}\right)\)
= \(\frac{x}{x-3}-\frac{x^2+3x}{2x+3}\cdot\left(\frac{\left(x+3\right)^2}{x\left(x-3\right)\left(x+3\right)}-\frac{x^2}{x\left(x-3\right)9x+3)}\right)\)
= \(\frac{x}{x-3}-\frac{x^2+3x}{2x+3}\cdot\left(\frac{\left(x+3\right)^2-x^2}{x\left(x-3\right)\left(x+3\right)}\right)\)
\(=\frac{x}{x-3}-\frac{x^2+3x}{2x+3}\cdot\left(\frac{x^2+6x+9-x^2}{x\left(x-3\right)\left(x+3\right)}\right)\)
\(=\frac{x}{x-3}-\frac{x^2+3x}{2x+3}\cdot\left(\frac{3\left(2x+3\right)}{x\left(x-3\right)\left(x+3\right)}\right)\)
\(=\frac{x}{x-3}-\frac{3}{x-3}\)
= \(\frac{x-3}{x-3}=1\)
2) ĐKXĐ: x≠0;x≠3;x≠-3;x≠\(-\frac32\)
\(\Leftrightarrow\frac{x^2-6}{x-3}+\frac{x^2+3}{2x+3}\left(\frac{x}{\left(x-3\right)\left(x+3\right)}-\frac{\left(x+3\right)^2}{x\left(x-3\right)\left(x+3\right)}\right)\)
\(=\frac{x^2-6}{x-3}+\frac{x^2+3}{2x+3}\cdot\left(\frac{x^2-\left(x+3\right)^2}{x\left(x-3\right)\left(x+3\right)}\right)\)
= \(\frac{x^2-6}{x-3}+\frac{x^2+3}{2x+3}\cdot\left(\frac{-3\left(2x+3\right)}{x\left(x-3\right)\left(x+3\right)}\right)\)
= \(\frac{x^2-6}{2x+3}\cdot\frac{-3\left(2x+3\right)}{x\left(x-3\right)\left(x+3\right)}=\frac{-3\left(x^2+3\right)}{x\left(x-3\right)\left(x+3\right)}\)
\(=\frac{x\left(x+3\right)\left(x^2-6\right)-3\left(x^2+3\right)}{x\left(x-3\right)9x+3)}\)
= \(\frac{\left(x^2+3x\right)\left(x^2-6\right)-3x^2-9}{x\left(x-3\right)\left(x+3\right)}\)
= \(\frac{x^4+3x^3-9x^2-18x-9}{x\left(x-3\right)\left(x+3\right)}\)
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