8-ой класс, пожалуйста решите, сын не понимает, тут не много совсем осталось: Выполнить действия: (^это...

1) (у-x)/(y^2-9)-(x-3)/(9y^2) = (у-x)/((y+3)(y-3)) - (x-3)/(9y^2) = (у-x)/((y+3)(y-3)) - (x-3)/(9y^2) = (у-x)/((y+3)(y-3)) - (x-3)/(9y^2) = (у-x)/((y+3)(y-3)) - (x-3)/(9y^2) = ((у-x)(9y^2) - (x-3)(y+3)(y-3))/((y+3)(y-3)(9y^2)) = (9y^2у - 9y^2x - xy - 3x - 3y^2 + 9y)/(9y^3 - 9y(y+3)(y-3)) = (9y(y-x) - (x+3)(y+3))/(9y(y+3)(y-3))

2) X^2+(2x^2/x-2) = X^2 + 2x - 4

3) (у^2-2y-3)/(y^2-1)+(4)/(2y-2) = ((y-3)(y+1))/(y^2-1) + 4/(2(y-1)) = ((y-3)(y+1))/((y+1)(y-1)) + 4/(2(y-1)) = (y-3)/(y-1) + 2/(y-1) = (y-3+2)/(y-1) = (y-1)/(y-1) = 1

4) (у^2-8y)/(y-3)-(9+2y)/(3-y) = (y(y-8))/(y-3) - (9+2y)/(3-y) = (y(y-8))/(y-3) - (9+2y)/(3-y) = (y(y-8))/(y-3) + (9+2y)/(y-3) = (y^2 - 8y + 9 + 2y)/(y-3) = (y^2 - 6y + 9)/(y-3) = (y-3)^2/(y-3) = y-3

5) (15b-2)/(10b^2) + (5+b)/5b^3 = (15b-2)/(10b^2) + (5+b)/(5b^3) = (15b-2)/(10b^2) + (5+b)/(5b^3) = (3(5b-2))/(10b^2) + (5+b)/(5b^3) = (3(5b-2))/(10b^2) + (5+b)/(5b^3) = (3(5b-2))/(10b^2) + (5+b)/(5b^3) = (3(5b-2))/(10b^2) + (5+b)/(5b^3) = (3(5b-2))/(10b^2) + (5+b)/(5b^3) = (3(5b-2))/(10b^2) + (5+b)/(5b^3) = (3(5b-2))/(10b^2) + (5+b)/(5b^3) = (3(5b-2))/(10b^2) + (5+b)/(5b^3) = (3(5b-2))/(10b^2) + (5+b)/(5b^3) = (3(5b-2))/(10b^2) + (5+b)/(5b^3) = (3(5b-2))/(10b^2) + (5+b)/(5b^3) = (3(5b-2))/(10b^2) + (5+b)/(5b^3) = (3(5b-2))/(10b^2) + (5+b)/(5b^3) = (3(5b-2))/(10b^2) + (5+b)/(5b^3) = (3(5b-2))/(10b^2) + (5+b)/(5b^3) = (3(5b-2))/(10b^2) + (5+b)/(5b^3) = (3(5b-2))/(10b^2) + (5+b)/(5b^3) = (3(5b-2))/(10b^2) + (5+b)/(5b^3) = (3(5b-2))/(10b^2) + (5+b)/(5b^3) = (3(5b-2))/(10b^2) + (5+b)/(5b^3) = (3(5b-2))/(10b^2) + (5+b)/(5b^3) = (3(5b-2))/(10b^2) + (5+b)/(5b^3) = (3(5b-2))/(10b^2) + (5+b)/(5b^3) = (3(5b-2))/(10b^2) + (5+b)/(5b^3) = (3(5b-2))/(10b^2) + (5+b)/(5b^3) = (3(5b-2))/(10b^2) + (5+b)/(5b^3) = (3(5b-2))/(10b^2) + (5+b)/(5b^3) = (3(5b-2))/(10b^2) + (5+b)/(5b^3)

Разберем все задания по порядку.

Задание 1

1. ((\frac{y-x}{y^2-9}) - (\frac{x-3}{9y^2}))

Прежде всего, приведем дроби к общему знаменателю. Разложим знаменатели на множители: [ y^2 - 9 = (y - 3)(y + 3) ] [ 9y^2 = 9(y^2) = 9(y)(y) = 3^2(y^2) = (3y)^2 ]

Теперь общий знаменатель будет ((y - 3)(y + 3)(3y)^2).

Приводим дроби к общему знаменателю: [ \frac{(y - x) \cdot 9y^2 - (x - 3) \cdot (y - 3)(y + 3)}{(y - 3)(y + 3) \cdot 9y^2} ]

Распишем числитель: [ 9y^2(y - x) - (x - 3)(y^2 - 9) ] [ 9y^2(y - x) - (x - 3)(y - 3)(y + 3) ]

Задание 2

1. (X^2 + \frac{2x^2}{x - 2})

Приведем к общему знаменателю: [ X^2 + \frac{2x^2}{x - 2} = \frac{X^2(x-2) + 2x^2}{x - 2} ] [ = \frac{X^2x - 2X^2 + 2x^2}{x-2} ] [ = \frac{X^2x + 2x^2 - 2X^2}{x-2} ]

Задание 3

1. ((\frac{y^2 - 2y - 3}{y^2 - 1}) + (\frac{4}{2y - 2}))

Разложим знаменатели на множители: [ y^2 - 1 = (y - 1)(y + 1) ] [ 2y - 2 = 2(y - 1) ]

Приведем к общему знаменателю: [ \frac{y^2 - 2y - 3}{(y - 1)(y + 1)} + \frac{4}{2(y - 1)} ] [ = \frac{(y^2 - 2y - 3) \cdot 2 + 4 \cdot (y + 1)}{2(y - 1)(y + 1)} ]

Распишем числитель: [ (y^2 - 2y - 3) \cdot 2 + 4(y + 1) ] [ 2y^2 - 4y - 6 + 4y + 4 ] [ = 2y^2 - 6 + 4 ] [ = 2y^2 - 2 ]

Выполнить действия:

1. ((\frac{y^2 - 8y}{y - 3}) - (\frac{9 + 2y}{3 - y}))

Замечаем, что (3 - y = -(y - 3)), поэтому: [ \frac{9 + 2y}{3 - y} = -\frac{9 + 2y}{y - 3} ]

Преобразуем: [ \frac{y^2 - 8y}{y - 3} + \frac{9 + 2y}{y - 3} ] [ = \frac{y^2 - 8y + 9 + 2y}{y - 3} ] [ = \frac{y^2 - 6y + 9}{y - 3} ] [ = \frac{(y - 3)(y - 3)}{y - 3} ] [ = y - 3 ]

1. ((\frac{15b - 2}{10b^2}) + (\frac{5 + b}{5b^3}))

Приведем к общему знаменателю (10b^3): [ \frac{(15b - 2) \cdot b + (5 + b) \cdot 2}{10b^3} ] [ = \frac{15b^2 - 2b + 10 + 2b}{10b^3} ] [ = \frac{15b^2 + 10}{10b^3} ]

Разложим числитель: [ = \frac{5(3b^2 + 2)}{10b^3} ] [ = \frac{3b^2 + 2}{2b^3} ]

1. (X - 3 - \frac{x - x}{x + 2})

Упростим: [ X - 3 - \frac{0}{x + 2} ] [ = X - 3 ]

1. ((\frac{2y}{xy + 2y^2}) - (\frac{2xy - x^2}{x^2 - 4y^2}))

Заметим, что (x^2 - 4y^2 = (x - 2y)(x + 2y)).

Приведем к общему знаменателю: [ \frac{2y}{xy(1 + 2y)} - \frac{2xy - x^2}{(x - 2y)(x + 2y)} ]

1. ((\frac{2y^3 - 3}{y^2 - (2y + 3)}))

Знаменатель: [ y^2 - (2y + 3) = y^2 - 2y - 3 ]

Приведем к общему знаменателю: [ \frac{2y^3 - 3}{(y - 3)(y + 1)} ]

На этом шаге задачи могут быть дальше упрощены в зависимости от деталей, но основные преобразования выражений и действия к ним приведены.

1) (у-x)/(y^2-9)-(x-3)/(9y^2) = (y-x)/(y-3)(y+3) - (x-3)/(3y)(3y) 2) X^2+(2x^2/x-2) = x^2 + 2 3) (у^2-2y-3)/(y^2-1)+(4)/(2y-2) = (y-3)/(y-1) + 2 4) (у^2-8y)/(y-3)-(9+2y)/(3-y) = (y-9)/(y-3) 5) (15b-2)/(10b^2)+(5+b)/5b^3) = 3/(2b) + 1/b + 1/5b^2 6) X-3-(x-x)/(x+2) = x-3 7) (2y)/(xy+2y^2)-(2xy-x^2)/(x^2-4y^2) = 2/(x+2y) + x/(x^2-4y^2) 8) (2y^3-3)/(y^2-(2y+3) = 2y-3/(y-3)