11/12, 1/36, 113/45, 5/6, 11/9, 5/24, 7/12, 1/12
Пошаговое объяснение:№1. 1) 3/12 = 3 : 3/12 : 3 = 1/4;
2) 25/30 = 25 : 5/30 : 5 = 5/6;
3) 1/4 + 5/6 = (3 * 1)/12 + (2 * 5)/12 = 3/12 + 10/12 = 13/12 = 1 1/12.
ответ: 1 1/12.
№2. 1) 10/24 = 10 : 2/24 : 2 = 5/12;
2) 21/54 = 21 :3/54 : 3 = 7/18;
3) 5/12 - 7/18 = (3 * 5)/36 - (2 * 7)/36 = 15/36 - 14/36 = 1/36.
ответ: 1/36.
№3. 1) 30/54 = 30 : 6/54 : 6 = 5/9;
2) 22/30 = 22 : 2/30 : 2 = 11/15;
3) 5/9 + 11/15 = (5 * 5)/45 + (3 * 11)/45 = 25/45 + 33/45 = 58/45 = 1 13/45.
ответ: 1 13/45.
№4. 1) 28/40 = 28 : 4/40 : 4 = 7/10;
2) 10/75 = 10 : 5/75 : 5 = 2/15;
3) 7/10 + 2/15 = (3 * 7)/30 + (2 * 2)/30 = 21/30 + 4/30 = 25/30 = 25 : 5/30 : 5 = 5/6.
ответ: 5/6.
№5. 1) 12/27 = 12 : 3/27 : 3 = 4/9;
2) 14/21 = 14 : 7/21 : 7 = 2/3;
3) 4/9 + 2/3 = 4/9 + (3 * 2)/9 = 4/9 + 6/9 = 10/9 = 1 1/9.
ответ: 1 1/9.
№6. 1) 14/24 = 14 : 2/24 :2 = 7/12;
2) 15/40 = 15 : 5/40 : 5 = 3/8;
3) 7/12 - 3/8 = (2 * 7)/24 - (3 * 3)24 = 14/24 - 9/24 = 5/24.
ответ: 5/24.
№7. 1) 12/18 = 12 :6/18 : 6 = 2/3;
2) 5/60 = 5 : 5/60 : 5 = 1/12;
3) 2/3 - 1/12 = (4 * 2)/12 - 1/12 = 8/12 - 1/12 = 7/12.
ответ: 7/12.
№8. 1) 4/24 = 4 : 4/24 : 4 = 1/6;
2) 3/36 = 3 : 3/36 : 3 = 1/12;
3) 1/6 - 1/12 = (2 * 1)/12 - 1/12 = 2/12 - 1/12 = 1/12.
ответ: 1/12.
Пошаговое объяснение:
1) (a²+ab+c²+2ac+bc)/(a²-2bc-c²-b²)=((a²+2ac+c²)+(ab+bc))/(a²-(b²+2bc+c²))=((a+c)²+b(a+c))/(a²-(b+c)²)=((a+c)(a+b+c))/((a-b-c)(a+b+c))=(a+c)/(a-b-c)
2) (a²-c²-4ab+4b²)/(a²-4ab+ac+4b²-2bc)=((a²-4ab+4b²)-c²)/((a²-4ab+4b²)+(ac-2bc))=((a-2b)²-c²)/((a-2b)²+c(a-2b))=((a-2b-c)(a-2b+c))/((a-2b)(a-2b+c))=(a-2b-c)/(a-2b)
3) (y²-x²-25z²+10xz)/(2xy-5xz+x²-5yz+y²)=(y²-(x²-10xz+25z²))/((x²+2xy+y²)-(5xz+5yz))=(y²-(x-5z)²)/((x+y)²-5z(x+y))=((y-x+5z)(y+x-5z))/((x+y)(x+y-5z))=(-x+y+5z)/(x+y)=-(x-y-5z)/(x+y)
4) (x²+y²+6zx+2xy+6zx)/(y²-x²-12xz-36z²)=((x²+2xy+y²)+(6xz+6yz))/(y²-(x²+12xz+36z²))=((x+y)²+6z(x+y))/(y²-(x+6z)²)=((x+y)(x+y+6z))/((y-x-6z)(y+x+6z))=(x+y)/(-x+y-6z)=-(x+y)/(x-y+6z)