Упр.1.92 ГДЗ Дорофеев Суворова 8 класс (Алгебра)

а) (b/a-a/b) :(a+b);
б) (x^2-y^2 ) :(1/x+1/y);
в) (x/y+y/x-2) :(x-y);
г) (a+b)^2 :(1/a^2 +1/b^2 +2/ab).

а)

$$ \left(\frac{b}{a}-\frac{a}{b}\right):(a+b)=\frac{b^2-a^2}{ab}:(a+b)=\frac{(b-a)(b+a)}{ab}\cdot\frac{1}{a+b}=\frac{b-a}{ab}. $$

б)

$$ (x^2-y^2):\left(\frac{1}{x}+\frac{1}{y}\right)= (x-y)(x+y):\frac{x+y}{xy} $$
$$ =(x-y)(x+y)\cdot\frac{xy}{x+y}=xy(x-y). $$

в)

$$ \left(\frac{x}{y}+\frac{y}{x}-2\right):(x-y)=\frac{x^2+y^2-2xy}{xy}:(x-y) $$
$$ =\frac{(x-y)^2}{xy}:(x-y)=\frac{(x-y)^2}{xy}\cdot\frac{1}{x-y}=\frac{x-y}{xy}. $$

г)

$$ (a+b)^2:\left(\frac{1}{a^2}+\frac{1}{b^2}+\frac{2}{ab}\right) =(a+b)^2:\frac{b^2+a^2+2ab}{a^2b^2} $$
$$ =(a+b)^2:\frac{(a+b)^2}{a^2b^2} =(a+b)^2\cdot\frac{a^2b^2}{(a+b)^2}=a^2b^2. $$

Ответ

а) $$\frac{b-a}{ab}$$; б) $$xy(x-y)$$; в) $$\frac{x-y}{xy}$$; г) $$a^2b^2$$.