Toán Lớp 8: 6x/x^3-9x + 5x/x^2-3x + x/x^2+3x

Question

Toán Lớp 8:  6x/x^3-9x + 5x/x^2-3x + x/x^2+3x

danvanthu · Answer

Ta c&oacute;:    x^3 -9x = x(x^2 -9)=x(x-3)(x+3)   x^2 -3x=x(x-3)   x^2 +3x=x(x+3)   Quy đồng:   (6x)/(x^3-9x) = (6x)/(x(x-3)(x+3))    (5x)/(x^2-3x) = (5x(x+3))/(x(x-3)(x+3)) = (5x^2 +15x)/(x(x-3)(x+3))    x/(x^2 +3x) = (x(x-3))/(x(x-3)(x+3)) = (x^2 -3x)/(x(x-3)(x+3))     Vậy: (6x)/(x^3-9x) + (5x)/(x^2-3x) + x/(x^2 +3x)     = (6x)/(x(x-3)(x+3)) + (5x^2 +15x)/(x(x-3)(x+3)) + (x^2 -3x)/(x(x-3)(x+3))     = (6x+5x^2 +15x+x^2 -3x)/(x(x-3)(x+3))     = (6x^2 +18x)/(x(x-3)(x+3))     = (6x(x+3))/(x(x-3)(x+3))     = (6)/(x-3)

tuenhioanh · Answer

Giải đáp:    6/(x-3)     Lời giải và giải thích chi tiết:    (6x)/(x^3 -9x)+(5x)/(x^2 -3x)+ x/(x^2 +3x)   =(6x)/(x(x^2-9))+(5x)/(x(x-3))+ x/(x(x+3))   =6/(x^2-9)+ 5/(x-3) + 1/(x+3)   =6/((x-3)(x+3))+5/(x-3) +1/(x+3)   =(6+5(x+3)+x-3)/((x-3)(x+3))   =(6+5x+15+x-3)/((x-3)(x+3))   =(6x+18)/((x-3)(x+3))   =(6(x+3))/((x-3)(x+3))   =6/(x-3)