Алгебра 8 класс учебник Макарычев, Миндюк ответы – номер 42

а) a(x - 2y)/b(2y - x) = -a(2y - x)/b(2y - x) = -a(2y - x) : (2y - x)/b(2y - x) : (2y - x) = -a/b = -a/b
б) $$ \frac{5 x(x-y)}{x^3(y-x)}=\frac{-5 x(y-x)}{x^3(y-x)}=\frac{-5 x(y-x) \div x(y-x)}{x^3(y-x) \div x(y-x)}=\frac{-5}{x^2}=-\frac{5}{x^2} $$
в) 3a - 36/12b - ab = 3(a - 12)/-b(a - 12) = 3(a - 12) : (a - 12)/-b(a - 12) : (a - 12) = 3/-b = -3/b
г) $$ \frac{7 b-14 b^2}{42 b^2-21 b}=\frac{7 b(1-2 b)}{-21 b(1-2 b)}=\frac{7 b(1-2 b) \div 7 b(1-2 b)}{-21 b(1-2 b) \div 7 b(1-2 b)}=\frac{1}{-3}=-\frac{1}{3} $$
д) $$ \frac{25-a^2}{3 a-15}=\frac{5^2-a^2}{3 a-15} $$ = (5 - a)(5 + a)/-3(5 - a) = (5 - a)(5 + a) : (5 - a)/-3(5 - a) : (5 -a) = 5 + a/-3 = -5 + a/3
е) $$ \frac{3-3 x}{x^2-2 x+1}=\frac{3(1-x)}{(x-1)^2}= $$ = -3(x - 1)/(x - 1)(x - 1) = -3(x - 1) : (x - 1)/(x - 1)(x - 1) : (x - 1) = -3/x - 1 = -3/x - 1
ж) $$ \frac{8 b^2-8 a^2}{a^2-2 a b+b^2}=\frac{8\left(b^2-a^2\right)}{(a-b)^2}= $$ = 8(b - a)(b + a)/(a - b)(a - b) = -8(a - b)(b + a)/(a - b)(a - b) = -8(a - b)(b + a) : (a - b)/(a - b)(a - b) : (a - b) = -8(b + a)/a - b = --8(b + a)/a - b
з) $$ \frac{(b-2)^3}{(2-b)^2}=\frac{(b-2)^2(b-2)}{((-1)(b-2))^2}=\frac{(b-2)^2(b-2)}{(-1)^2(b-2)^2}=\frac{(b-2)^2(b-2) \div(b-2)^2}{(b-2)^2 \div(b-2)^2}=\frac{b-2}{1}=b-2 $$