Bài 1:
2: ĐKXĐ: \(x\notin\left\{3;-3\right\}\)
\(\dfrac{2}{x+3}+\dfrac{x}{3-x}-\dfrac{x-x^2}{x^2-9}\)
\(=\dfrac{2}{x+3}-\dfrac{x}{x-3}+\dfrac{x^2-x}{\left(x-3\right)\left(x+3\right)}\)
\(=\dfrac{2\left(x-3\right)-x\left(x+3\right)+x^2-x}{\left(x-3\right)\left(x+3\right)}\)
\(=\dfrac{2x-6-x^2-3x+x^2-x}{\left(x-3\right)\left(x+3\right)}\)
\(=\dfrac{-2x-6}{\left(x-3\right)\left(x+3\right)}=-\dfrac{2\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}=-\dfrac{2}{x-3}\)
3: ĐKXĐ: x<>1
\(\dfrac{2}{x-1}-\dfrac{7-x}{3x-3}\)
\(=\dfrac{2}{x-1}+\dfrac{x-7}{3\left(x-1\right)}\)
\(=\dfrac{6+x-7}{3\left(x-1\right)}=\dfrac{x-1}{3\left(x-1\right)}=\dfrac{1}{3}\)
5: ĐKXĐ: \(x\notin\left\{2;-2\right\}\)
\(\dfrac{1}{x-2}+\dfrac{1}{x+2}-\dfrac{4x-4}{x^2-4}\)
\(=\dfrac{1}{x-2}+\dfrac{1}{x+2}-\dfrac{4x-4}{\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{x+2+x-2-4x+4}{\left(x-2\right)\left(x+2\right)}=\dfrac{-2x+4}{\left(x-2\right)\left(x+2\right)}=\dfrac{-2}{x+2}\)
6: ĐKXĐ: \(x\notin\left\{0;3\right\}\)
\(\dfrac{x}{x-3}-\dfrac{9}{x^2-3x}\)
\(=\dfrac{x}{x-3}-\dfrac{9}{x\left(x-3\right)}\)
\(=\dfrac{x^2-9}{x\left(x-3\right)}=\dfrac{\left(x-3\right)\left(x+3\right)}{x\left(x-3\right)}=\dfrac{x+3}{x}\)
8: ĐKXĐ: \(x\notin\left\{2;-2\right\}\)
\(\dfrac{2}{x-2}+\dfrac{3}{x+2}-\dfrac{18-5x}{x^2-4}\)
\(=\dfrac{2}{x-2}+\dfrac{3}{x+2}+\dfrac{5x-18}{\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{2x+4+3x-6+5x-18}{\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{10x-20}{\left(x-2\right)\left(x+2\right)}=\dfrac{10\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}=\dfrac{10}{x+2}\)
9: ĐKXĐ: \(x\notin\left\{0;-3\right\}\)
\(\dfrac{x+1}{2x+6}+\dfrac{2x+3}{x^2+3x}\)
\(=\dfrac{x+1}{2\left(x+3\right)}+\dfrac{2x+3}{x\left(x+3\right)}\)
\(=\dfrac{x\left(x+1\right)+2\left(2x+3\right)}{2x\left(x+3\right)}\)
\(=\dfrac{x^2+x+4x+6}{2x\left(x+3\right)}=\dfrac{\left(x+2\right)\left(x+3\right)}{2x\left(x+3\right)}=\dfrac{x+2}{2x}\)
