高専の数学解説

第1章 1.20

(1)

(x+1)(x2−4x+4)(x−2)(x2+2x+1)=(x+1)(x−2)2(x−2)(x+1)2=x−2x+1\frac{(x+1)(x^2-4x+4)}{(x-2)(x^2+2x+1)}=\frac{(x+1)(x-2)^2}{(x-2)(x+1)^2}=\frac{x-2}{x+1}

(2)

x2−xy−6y2x2−5xy+6y2=(x−3y)(x+2y)(x−2y)(x−3y)=x+2yx−2y\frac{x^2-xy-6y^2}{x^2-5xy+6y^2}=\frac{(x-3y)(x+2y)}{(x-2y)(x-3y)}=\frac{x+2y}{x-2y}

(3)

6x3−6x2−12x3x3−12x=6x(x−2)(x+1)3x(x−2)(x+2)=2(x+1)x+2\frac{6x^3-6x^2-12x}{3x^3-12x}=\frac{6x(x-2)(x+1)}{3x(x-2)(x+2)}=\frac{2(x+1)}{x+2}

(4)

x3−x2−20xx3−x2−2x=x(x−5)(x+4)x(x−2)(x+1)=(x−5)(x+4)(x−2)(x+1)=x2−x−20x2−x−2\frac{x^3-x^2-20x}{x^3-x^2-2x}=\frac{x(x-5)(x+4)}{x(x-2)(x+1)}=\frac{(x-5)(x+4)}{(x-2)(x+1)}=\frac{x^2-x-20}{x^2-x-2}

解説: r31bn1z