Упр.8.20 ГДЗ Мордкович 8 класс (Алгебра)

б) (x^-2 — y^-2):(x-y);
в) (m^-2 + n^-2):(m2+n2);
г) (ab^-2 + a^-2b)*(a^-1/b)^-2.

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

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

3. $$ (m^{-2}+n^{-2}):(m^2+n^2) =\left(\frac{1}{m^2}+\frac{1}{n^2}\right):(m^2+n^2) =\frac{m^2+n^2}{m^2n^2}:\,(m^2+n^2) =\frac{1}{m^2n^2}. $$

4. $$ (ab^{-2}+a^{-2}b)\cdot\left(\frac{a^{-1}}{b}\right)^{-2} =\left(\frac{a}{b^2}+\frac{b}{a^2}\right)\cdot\left(\frac{1}{ab}\right)^{-2} =\frac{a^3+b^3}{a^2b^2}\cdot a^2b^2 =a^3+b^3. $$

Ответ

а) $$\frac{1}{ab}$$; б) $$-\frac{x+y}{x^2y^2}$$; в) $$\frac{1}{m^2n^2}$$; г) $$a^3+b^3$$.