Question

Представьте в виде дроби выражение 1/(x-2)(x-1)+1/(х-1)x+1/x(x+1)+1/(x+1)(x+2)

Answer 1

(x+1)(x+2)+(x-2)(x-1) / (x-2)(x-1)(x+1)(x+2) + (x+1)+(x-1) / x(x-1)(x+1) =

x^2+2x+x+2+x^2-x-2x+2 / (x-2)(x-1)(x+1)(x+2) + x+1+x-1 / x(x-1)(x+1) =

2x^2+4 / (x-2)(x-1)(x+1)(x+2) + 2x / x(x-1)(x+1) =

2x^3+4x+2x(x-2)(x+2) / x(x-2)(x-1)(x+1)(x+2) =

2x^3+4x+2x^3-8x / x(x-2)(x-1)(x+1)(x+2) =

4x(x-1)(x+1) / x(x-2)(x-1)(x+1)(x+2) = 4 / (x-2)(x+2)