Toán Lớp 8: tính `(3x+2)/(x^2-2x+1)-6/(x^2-1)-(3x-2)/(x^2+2x+1)`

Question

Toán Lớp 8:  tính (3x+2)/(x^2-2x+1)-6/(x^2-1)-(3x-2)/(x^2+2x+1)

lanhuongthu · Answer

(3x+2)/(x^2 - 2x+1) - 6/(x^2-1) - (3x-2)/(x^2+2x+1)   =  (3x+2)/((x-1)^2) - 6/((x-1)(x+1)) - (3x-2)/((x+1)^2)   =  ( (3x+2) (x+1)^2 - 6 (x+1)(x-1) - (3x-2)(x-1)^2))/((x-1)^2 . (x+1)^2)   = ( (3x+2)(x^2 + 2x+1) - 6 (x^2 - 1) - (3x-2)(x^2 - 2x+1))/((x-1)(x-1)(x+1)(x+1))   = ( (3x^3 + 8x^2 + 7x+2) - (6x^2 - 6) - (3x^3 - 8x^2 + 7x-2))/((x^2-1)(x^2-1))   =  (3x^3+  8x^2 + 7x + 2 - 6x^2 + 6 - 3x^3 + 8x^2 - 7x+2)/((x^2-1)(x^2-1))   =  (10x^2 + 10)/(x^4 - 2x^2 +1)

ngoclankhue · Answer

Giải đáp+Lời giải và giải thích chi tiết:     (3x+2)/(x^2 - 2x +1) - 6/(x^2-1) - (3x-2)/(x^2 + 2x +1)   =(3x+2)/((x-1)^2) - 6/(x^2-1) - (3x-2)/((x+1)^2)   =((3x+2)(x+1)^2-6(x^2 -1) -(3x-2)(x-1)^2)/((x^2-1)^2)    =((3x+2)(x^2 + 2x +1) - 6x^2+6 -(3x-2)(x^2-2x+1))/((x^2-1)^2)    = (3x^3 + 6x^2 + 3x + 2x^2 + 4x + 2 - 6x^2+6 -3x^3 + 6x^2 - 3x + 2x^2 - 4x +2)/((x^2-1)^2)    =(10x^2 +10)/(x^4 - 2x^2 +1)