Question

Срочно!!!!! 155 Б и Г, 156 весь пожалуйста помогите!

Answer 1

155.
б)
$frac{xy-1.2y^2}{x^2-1.2xy} + frac{x^2+0.4xy}{xy+0.4y^2} = frac{y(x-1.2y)}{x(x-1.2y)} + frac{x(x+0.4y)}{y(x+0.4y)} = frac{y} {x}+ frac{x}{y}= frac{x^2+y^2}{xy}$

г) смотри скан, возможно, я где-то ошиблась, т.к. длинновата концовка

156
а)
$frac{1}{(a-b)(a-c)}+ frac{1}{(b-c)(b-a)}+ frac{1}{(c-a)(c-b)}= \ frac{1}{(a-b)(a-c)}- frac{1}{(b-c)(a-b)}-frac{1}{(a-c)(c-b)}= \ frac{1}{(a-b)(a-c)}- frac{1}{(b-c)(a-b)}+frac{1}{(a-c)(b-c)}= \ frac{b-c}{(a-b)(a-c)(b-c)}- frac{a-c}{(a-b)(a-c)(b-c)}+frac{a-b}{(a-b)(a-c)(b-c)}= \ frac{b-c-a+c+a-b}{(a-b)(a-c)(b-c)}= frac{0}{(a-b)(a-c)(b-c)}= 0$

б)
$frac{a}{(a-b)(a-c)}+ frac{b}{(b-c)(b-a)}+ frac{c}{(c-a)(c-b)}= \ frac{a}{(a-b)(a-c)}- frac{b}{(b-c)(a-b)}-frac{c}{(a-c)(c-b)}= \ frac{a}{(a-b)(a-c)}- frac{b}{(b-c)(a-b)}+frac{c}{(a-c)(b-c)}= \ frac{a(b-c)}{(a-b)(a-c)(b-c)}- frac{b(a-c)}{(a-b)(a-c)(b-c)}+frac{c(a-b)}{(a-b)(a-c)(b-c)}= \ frac{a(b-c)-b(a-c)+c(a-b)}{(a-b)(a-c)(b-c)}=frac{ab-ac-ab+bc+ac-bc}{(a-b)(a-c)(b-c)}= \ frac{0}{(a-b)(a-c)(b-c)}= 0$ 

в)
$frac{a^2}{(a-b)(a-c)}+ frac{b^2}{(b-c)(b-a)}+ frac{c^2}{(c-a)(c-b)}= \ frac{a^2}{(a-b)(a-c)}- frac{b^2}{(b-c)(a-b)}-frac{c^2}{(a-c)(c-b)}= \ frac{a^2}{(a-b)(a-c)}- frac{b^2}{(b-c)(a-b)}+frac{c^2}{(a-c)(b-c)}= \ frac{a^2(b-c)}{(a-b)(a-c)(b-c)}- frac{b^2(a-c)}{(a-b)(a-c)(b-c)}+frac{c^2(a-b)}{(a-b)(a-c)(b-c)}= \ frac{a^2(b-c)-b^2(a-c)+c^2(a-b)}{(a-b)(a-c)(b-c)}=frac{a^2b-a^2c-ab^2+b^2c+ac^2-bc^2}{(a-b)(a-c)(b-c)}= \ frac{a^2b-a^2c-ab^2+b^2c+ac^2-bc^2}{(a^2-ac-ab+bc)(b-c)}=$
$frac{a^2b-a^2c-ab^2+b^2c+ac^2-bc^2}{a^2b-a^2c-abc+ac^2-ab^2+abc+b^2c-bc^2}= \ frac{a^2b-a^2c-ab^2+b^2c+ac^2-bc^2}{a^2b-a^2c+ac^2-ab^2+b^2c-bc^2} \ frac{a^2b-a^2c-ab^2+b^2c+ac^2-bc^2}{a^2b-a^2c-ab^2+b^2c+ac^2-bc^2}=1$