a: ĐKXĐ: \(x\notin\left\{2;-2;-3\right\}\)\(\dfrac{3x+9}{x^2-4}:\dfrac{x+3}{x-2}\)\(=\dfrac{3\left(x+3\right)}{\left(x-2\right)\left(x+2\right)}\cdot\dfrac{x-2}{x+3}\)\(=\dfrac{3}{x+2}\)b: ĐKXĐ:\(x\ne\pm2y\)\(\dfrac{5x^2+10xy}{x^2+2xy+4y^2}:\dfrac{x+2y}{x^3-8y^3}\)\(=\dfrac{5x\left(x+2y\right)}{x^2+2xy+4y^2}\cdot\dfrac{\left(x-2y\right)\left(x^2+2xy+4y^2\right)}{x+2y}\)\(=5x\left(x-2y\right)\)c: ĐKXĐ: \(x\notin\left\{3;-2;-3;-1\right\}\)\(\dfrac{x+1}{x-3}:\dfrac{x+2}{x+3}:\dfrac{x+3}{x+1}\)\(=\dfrac{x+1}{x-3}\cdot\dfrac{x+3}{x+2}\cdot\dfrac{x+1}{x+3}\)\(=\dfrac{\left(x+1\right)^2}{\left(x-3\right)\left(x+2\right)}\)d: ĐKXĐ: \(x\notin\left\{0;\dfrac{1}{2}\right\}\)\(\dfrac{4x^2+1}{x}:\left(1-2x\right)\)\(=\dfrac{4x^2+1}{x\cdot\left(1-2x\right)}\)\(=\dfrac{4x^2+1}{x-2x^2}\)Câu trả lời: a: ĐKXĐ: \(x\notin\left\{2;-2;-3\right\}\)\(\dfrac{3x+9}{x^2-4}:\dfrac{x+3}{x-2}\)\(=\dfrac{3\left(x+3\right)}{\left(x-2\right)\left(x+2\right)}\cdot\dfrac{x-2}{x+3}\)\(=\dfrac{3}{x+2}\)b: ĐKXĐ:\(x\ne\pm2y\)\(\dfrac{5x^2+10xy}{x^2+2xy+4y^2}:\dfrac{x+2y}{x^3-8y^3}\)\(=\dfrac{5x\left(x+2y\right)}{x^2+2xy+4y^2}\cdot\dfrac{\left(x-2y\right)\left(x^2+2xy+4y^2\right)}{x+2y}\)\(=5x\left(x-2y\right)\)c: ĐKXĐ: \(x\notin\left\{3;-2;-3;-1\right\}\)\(\dfrac{x+1}{x-3}:\dfrac{x+2}{x+3}:\dfrac{x+3}{x+1}\)\(=\dfrac{x+1}{x-3}\cdot\dfrac{x+3}{x+2}\cdot\dfrac{x+1}{x+3}\)\(=\dfrac{\left(x+1\right)^2}{\left(x-3\right)\left(x+2\right)}\)d: ĐKXĐ: \(x\notin\left\{0;\dfrac{1}{2}\right\}\)\(\dfrac{4x^2+1}{x}:\left(1-2x\right)\)\(=\dfrac{4x^2+1}{x\cdot\left(1-2x\right)}\)\(=\dfrac{4x^2+1}{x-2x^2}\)