a: ĐKXĐ: \(x\notin\left\{1;0;-2\right\}\)
\(\dfrac{1-x^2}{x^2+2x}:\dfrac{2-2x}{3x}\)
\(=\dfrac{\left(1-x\right)\left(1+x\right)}{x\left(x+2\right)}\cdot\dfrac{3x}{2\left(1-x\right)}\)
\(=\dfrac{3\left(1+x\right)}{2x}\)
b: ĐKXĐ: \(x\ne1\)
\(\dfrac{x^3+1}{x-1}:\left(x^2-x+1\right)\)
\(=\dfrac{\left(x+1\right)\left(x^2-x+1\right)}{\left(x-1\right)\left(x^2-x+1\right)}\)
\(=\dfrac{x+1}{x-1}\)
c: ĐKXĐ: \(x\notin\left\{-1;-2;0;2\right\}\)
\(\dfrac{x^2-x-2}{x^2+3x+2}:\dfrac{x^2-4x+4}{x^2+2x}\)
\(=\dfrac{\left(x-2\right)\left(x+1\right)}{\left(x+1\right)\left(x+2\right)}\cdot\dfrac{x\left(x+2\right)}{\left(x-2\right)^2}\)
\(=\dfrac{x}{x-2}\)
d: \(\dfrac{x-2y}{x^2-xy+y^2}:\dfrac{x^2-4xy+4y^2}{x^3+y^3}\)
\(=\dfrac{x-2y}{x^2-xy+y^2}\cdot\dfrac{\left(x+y\right)\left(x^2-xy+y^2\right)}{\left(x-2y\right)^2}\)
\(=\dfrac{x+y}{x-2y}\)
a) \(\dfrac{1-x^2}{x^2+2x}:\dfrac{2-2x}{3x}\left(x\ne1;0;-2\right)\)
\(=\dfrac{\left(1+x\right)\left(1-x\right)}{x\left(x+2\right)}:\dfrac{2\left(1-x\right)}{3x}\)
\(=\dfrac{\left(1+x\right)\left(1-x\right)}{x\left(x+2\right)}\cdot\dfrac{3x}{2\left(1-x\right)}\)
\(=\dfrac{3\left(x+1\right)}{2\left(x+2\right)}\)
\(=\dfrac{3x+3}{2x+4}\)
b) \(\dfrac{x^3+1}{x-1}:\left(x^2-x+1\right)\left(x\ne1\right)\)
\(=\dfrac{\left(x+1\right)\left(x^2-x+1\right)}{x-1}:\left(x^2-x+1\right)\)
\(=\dfrac{\left(x+1\right)\left(x^2-x+1\right)}{x-1}\cdot\dfrac{1}{x^2-x+1}\)
\(=\dfrac{x+1}{x-1}\)
c) \(\dfrac{x^2-x-2}{x^2+3x+2}:\dfrac{x^2-4x+4}{x^2+2x}\left(x\ne-1;-2;0;2\right)\)
\(=\dfrac{\left(x-2\right)\left(x+1\right)}{\left(x+2\right)\left(x+1\right)}:\dfrac{\left(x-2\right)^2}{x\left(x+2\right)}\)
\(=\dfrac{x-2}{x+2}\cdot\dfrac{x\left(x+2\right)}{\left(x-2\right)^2}\)
\(=\dfrac{x}{x-2}\)
d) \(\dfrac{x-2y}{x^2-xy+y^2}:\dfrac{x^2-4xy+4y^2}{x^3+y^3}\left(x\ne2y;-y\right)\)
\(=\dfrac{x-2y}{x^2-xy+y^2}:\dfrac{\left(x-2y\right)^2}{\left(x+y\right)\left(x^2-xy+y^2\right)}\)
\(=\dfrac{x-2y}{x^2-xy+y^2}\cdot\dfrac{\left(x+y\right)\left(x^2-xy+y^2\right)}{\left(x-2y\right)^2}\)
\(=\dfrac{x+y}{x-2y}\)
