Упр.4.52 ГДЗ Мордкович 8 класс (Алгебра)

а)

$$\frac{1}{(b-5)^2}-\frac{2}{b^2-25}+\frac{1}{(b+5)^2} = \frac{(b+5)^2-2(b^2-25)+(b-5)^2}{(b-5)^2(b+5)^2}$$

$$= \frac{b^2+10b+25-2b^2+50+b^2-10b+25}{(b-5)^2(b+5)^2} = \frac{100}{(b-5)^2(b+5)^2}$$

б)

$$\frac{1}{(2m-5n)^2}-\frac{2}{25n^2-4m^2}+\frac{1}{(5n+2m)^2} = \frac{(5n+2m)^2-2(25n^2-4m^2)+(5n-2m)^2}{(5n-2m)^2(5n+2m)^2}$$

$$= \frac{25n^2+20mn+4m^2-50n^2+8m^2+25n^2-20mn+4m^2}{(5n-2m)^2(5n+2m)^2} = \frac{16m^2}{(5n-2m)^2(5n+2m)^2}$$

Ответ

а) $$\frac{100}{(b-5)^2(b+5)^2}$$;
б) $$\frac{16m^2}{(5n-2m)^2(5n+2m)^2}$$.