中二數學4題,20分██████████████████████████████████████████████████ @ oob73zj92b的部落格

標題:

中二數學4題,20分██████████████████████████████████████████████████

發問:

求步驟。 1. ax-a^2/a-b+bx-ab/b-a 答案: x-a 2. 1/a+b-3/2b 答案: -3a+b/2b(a+b) 3. 5/4x+6-7/6x+9 答案: 1/6(2x+3) 4. 2x+y/x-y+y/2y-2x-x/x-y 答案: 2x+y/2(x-y)

最佳解答:

1. ax-a^2/a-b+bx-ab/b-a = ax-a^2/b-a/a-b+ bx-ab/-(a-b) <---optional =ax-a^2/b-a/a-b- bx-ab/a-b =(ax-a^2)-(bx-ab)/a-b =a(x-a)-b(x-a)/a-b =(x-a)(a-b)/a-b =x-a 2. 1/a+b-3/2b =2b-3(a+b)/2b(a+b) =2b-3a-3b/2b(a+b) =-3a-b/2b(a+b) 3. 5/4x+6-7/6x+9 =5/2(2x+3) - 7/3(2x+3) =5*3-7*2/6(2x+3) =15-14/6(2x+3) =1/6(2x+3) 4. 2x+y/x-y+y/2y-2x-x/x-y =2x+y/x-y+y/-2(x-y)-x/x-y =2x+y/x-y-y/2(x-y)-x/x-y =2(2x+y)-y-2x/2(x-y) =4x+2y-y-2x/2(x-y) =2x+y/2(x-y)

其他解答:

1. ax-a^2/a-b+bx-ab/b-a =ax-a^2-bx+ab/a-b =x(a-b)-a(a-b)/a-b =(x-a)(a-b)/a-b =x-a 2. 1/a+b-3/2b =2b-3(a+b)/2b(a+b) =2b-3a-3b/2b(a+b) =-(3a+b)/2b(a+b) 3. 5/4x+6-7/6x+9 =5(6x+9)-7(4x+6)/(4x+6)(6x+9) =30x+45-28x-42/24x^2+36x+36x+54 =2x+3/24x^2+72x+54 =2x+3/6(4x^2+12x+9) 1/6(2x+3) 4. 2x+y/x-y+y/2y-2x-x/x-y =2x+y-x/x-y + y/2y-2x =x+y/x-y + y/2(y-x) =x+y/x-y - y/2(x-y) =2x+2y-y/2(x-y) =2x+y/2(x-y)