`\frac{x+2}{x+3}-\frac{5}{x^2+x-6}+\frac{1}{2-x}` (ĐKXĐ: `x\ne2, x\ne-3` )
`=\frac{(x+2)(x-2)}{(x+3)(x-2)}-\frac{5}{x^2+3x-2x-6}-\frac{x+3}{(x+3)(x-2)}`
`=\frac{x^2-4}{(x+3)(x-2)}-\frac{5}{x.(x+3)-2(x+3)}-\frac{x+3}{(x+3)(x-2)}`
`=\frac{x^2-4}{(x+3)(x-2)}-\frac{5}{(x+3)(x-2)}-\frac{x+3}{(x+3)(x-2)}`
`=\frac{x^2-4-5-x-3}{(x+3)(x-2)}`
`=\frac{x^2-x-12}{(x+3)(x-2)}`
`=\frac{x^2-4x+3x-12}{(x+3)(x-2)}`
`=\frac{x(x-4)+3(x-4)}{(x+3)(x-2)}`
`=\frac{(x-4)(x+3)}{(x+3)(x-2)}`
`=\frac{x-4}{x-2}.`
