Simplification (x ^ 3-1) / (x ^ 3 + 2x ^ 2 + 2x + 1) + (x ^ 3 + 1) / (x ^ 3-2x ^ 2 + 2x-1) - (2x ^ 2 + 2) / (x ^ 2-1) method: simplification before general division

Simplification (x ^ 3-1) / (x ^ 3 + 2x ^ 2 + 2x + 1) + (x ^ 3 + 1) / (x ^ 3-2x ^ 2 + 2x-1) - (2x ^ 2 + 2) / (x ^ 2-1) method: simplification before general division

Original formula = (x-1) (x ^ 2 + X + 1) / [(x + 1) (x ^ 2-x + 1) + 2x (x + 1)] + (x + 1) (x ^ 2-x + 1) / [(x-1) (x ^ 2 + X + 1) - 2x (x-1)] - 2 (x ^ 2 + 1) / (x + 1) (x-1)
=(x-1)(x^2+x+1)/(x+1)(x^2+x+1)+(x+1)(x^2-x+1)/(x-1)(x^2-x+1)-2(x^2+1)/(x+1)(x-1)
=(x-1)/(x+1)+(x+1)/(x-1)-2(x^2+1)/(x+1)(x-1)
=[(x-1)^2+(x+1)^2-2(x^2+1)]/(x+1)(x-1)
=(x^2-2x+1+x^2+2x+1-2X^2-2)/(x+1)(x-1)
=0

General (2-x) / (4-2x) and (2x) / (x ^ 2-4)

A:
(2-x)/(4-2x)
=(x-2)/(2x-4)
=(x-2)(x+2)/[2(x-2)(x+2)]
=(x^2-4)/[2(x^2-4)]
(2x)/(x^2-4)
=4x/[2(x^2-4)]

1 / x ^ 2 + X, - 1 / x ^ + 2x + 1
/What fraction of a semicolon

x²+x=x(x+1)
x²+2x+1=(x+1)²
So 1 / (X & # 178; + x) = (x + 1) / X (x + 1) &# 178;
-1/(x²+2x+1)=-x/[x(x+1)²]

Given that the function g (x) = - x2-3, f (x) is a quadratic function, when x ∈ [- 1,2], the minimum value of F (x) is 1, and f (x) + G (x) is an odd function, the analytic expression of F (x) is obtained

Let f (x) = AX2 + BX + C (a ≠ 0), then f (x) + G (x) = (A-1) x2 + BX + C-3, ∵ f (x) + G (x) is an odd function, ∵ a = 1, C = 3 ∵ f (x) = x2 + BX + 3, symmetry axis X = - B2, when - B2 > 2, that is, B < - 4, f (x) is a decreasing function on [- 1, 2], and the minimum value of ∵ f (x) is f (2