Question

计算：(x^3-3x^2)/(x^2+5x+6)÷(x^3-9x)/(x^2+2x-3)*(x+2)/(2x)

(1)/(a-1)+(1)/(a+1)-(a^2+1)/(a^2-1)

Answer 1

1.(x^3-3x^2)/(x^2+5x+6)÷(x^3-9x)/(x^2+2x-3)*(x+2)/(2x)
=x^2(x-3)/(x+2)(x+3) * (x+3)(x-1)/x(x+3)(x-3) * (x+2)/2x
=(x-1)/2(x+3)
(1)/(a-1)+(1)/(a+1)-(a^2+1)/(a^2-1)
=(a+1+a-1)/(a²-1)-(a²+1)/(a²-1)
=(a²+2a+1)/(a²-1)
=(a+1)²/(a-1)(a+1)
=(a+1)/(a-1)

Answer 2

(x^3-3x^2)/(x^2+5x+6)÷(x^3-9x)/(x^2+2x-3)*(x+2)/(2x)
=【(x-1)(x-2)】/【（x+2)(x+3)】÷x（x^2-9)/(x+3)(x-1)*(x+2)/(2x)
=【(x-1)(x-2)】/【（x+2)(x+3)】÷[x（x+3)(x-3)/(x+3)(x-1)*(x+2)/(2x)]
=【(x-1)(x-2)】/【（x+2)(x+3)】*(x+3)(x-1)/x（x+3)(x-3))*(x+2)/(2x)]
=(x-1)^2(x-2)/[2x^2(x-3)(x+3)

(1)/(a-1)+(1)/(a+1)-(a^2+1)/(a^2-1)
=(a+1+a-1)/(a²-1)-(a²+1)/(a²-1)
=(a²+2a+1)/(a²-1)
=(a+1)²/(a-1)(a+1)
=(a+1)/(a-1)

Answer 3

(1)/(a-1)+(1)/(a+1)-(a^2+1)/(a^2-1)
=(a+1+a-1)/(a²-1)-(a²+1)/(a²-1)
=(a²+2a+1)/(a²-1)
=(a+1)²/(a-1)(a+1)
=(a+1)/(a-1)
上面那个实在是看不明白/、÷、*这些操作符，哪个上哪个下都不知道

追问

(x^2+5x+6)分之(x^3-3x^2)除(x^2+2x-3)分之(x^3-9x)乘(2x)分之(x+2)

Answer 4

2a/(a**2-1)-(a**2+1)/(a**2-1)
=-(a^2-2a+1)/(a^2-1)
=-(a-1)/(a+1)
=(1-a)/(a+1)

Answer 5

x^3-3x^2=x(x^2-9)(配平方)；x^2+5x+6=（x+2）（x+3）；x^2+2x-3=（x-1）（x+3）

原题=[x(x^2-9)]/[（x+2）（x+3）（x+3）]÷[x(x^2-9)]/（x-1）（x+3）×（x+2）/2x
=（x-1）/2（x+3）