a: \(\frac{x^2y^3}{5}=\frac{x^2y^3\cdot7xy}{5\cdot7xy}=\frac{7x^3y^4}{35xy}\)
b: \(\frac{x^2\left(x+2\right)}{x\left(x+2\right)^2}=\frac{x^2\left(x+2\right):\left\lbrack x\left(x+2\right)\right\rbrack}{x\left(x+2\right)^2:\left\lbrack x\left(x+2\right)\right\rbrack}=\frac{x}{x+2}\)
c: \(\frac{3-x}{3+x}=\frac{\left(3-x\right)\left(3-x\right)}{\left(3+x\right)\left(3-x\right)}=\frac{9-6x+x^2}{9-x^2}\)
d: \(\frac{x^3-4x}{10-5x}=\frac{x\left(x^2-4\right)}{-5\left(x-2\right)}=\frac{x\left(x+2\right)\left(x-2\right)}{-5\left(x-2\right)}=\frac{x\left(x+2\right)}{-5}=\frac{-x^2-2x}{5}\)
f: \(\frac{3x\left(x+5\right)}{2\left(x+5\right)}=\frac{3x\left(x+5\right):\left(x+5\right)}{2\left(x+5\right):\left(x+5\right)}=\frac{3x}{2}\)
g: \(\frac{x+2}{x-1}=\frac{\left(x+2\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}=\frac{\left(x+2\right)\left(x+1\right)}{x^2-1}\)
h: \(\frac{x^2-x-2}{x+1}=\frac{\left(x-2\right)\left(x+1\right)}{x+1}=x-2\)
\(\frac{x^2-3x+2}{x-1}=\frac{\left(x-1\right)\left(x-2\right)}{x-1}=x-2\)
Do đó: \(\frac{x^2-x-2}{x+1}=\frac{x^2-3x+2}{x-1}\)
i: \(\frac{x^3+8}{x^2-2x+4}=\frac{\left(x+2\right)\left(x^2-2x+4\right)}{x^2-2x+4}=x+2\)
