Với `x \ne +-2` có:
`M=[x^3]/[x^2-4]-x/[x-2]-2/[x+2]`
`M=[x^3-x(x+2)-2(x-2)]/[(x-2)(x+2)]`
`M=[x^3-x^2-2x-2x+4]/[(x-2)(x+2)]`
`M=[x^3-x^2-4x+4]/[(x-2)(x+2)]`
`M=[x^2(x-1)-4(x-1)]/[x^2-4]`
`M=[(x-1)(x^2-4)]/[x^2-4]`
`M=x-1`
\(M=\dfrac{x^3}{x^2-4}-\dfrac{x}{x-2}-\dfrac{2}{x+2}\)
\(=\dfrac{x^3-x\left(x+2\right)-2\left(x-2\right)}{x^2-4}\)
\(=\dfrac{x^3-x^2-2x-2x+4}{x^2+4}=\dfrac{x^3-4x-x^2+4}{x^2-4}=\dfrac{x\left(x^2-4\right)-\left(x^2-4\right)}{x^2-4}\)
\(=\dfrac{\left(x^2-4\right)\left(x-1\right)}{x^2-4}=x-1\)
Với x≠±2x≠±2 có:
M=x3x2−4−xx−2−2x+2M=x3x2-4-xx-2-2x+2
M=x3−x(x+2)−2(x−2)(x−2)(x+2)M=x3-x(x+2)-2(x-2)(x-2)(x+2)
M=x3−x2−2x−2x+4(x−2)(x+2)M=x3-x2-2x-2x+4(x-2)(x+2)
M=x3−x2−4x+4(x−2)(x+2)M=x3-x2-4x+4(x-2)(x+2)
M=x2(x−1)−4(x−1)x2−4M=x2(x-1)-4(x-1)x2-4
M=(x−1)(x2−4)x2−4M=(x-1)(x2-4)x2-4
M=x−1M=x-1
