Упр.950 ГДЗ Никольский Потапов 7 класс (Алгебра)

б) (m-1/n)/(n+1/m);
в) (1/a+1b)/(1/a-1/b);
г) (a/b-m/n)/(a/b+m/n);
д) ((a+b)/(a-b))/((a+b)2/(a2-b2);
е) (1/(1-m) + 1/(1+m))/ (1/(1-m) — 1/(1+m));
ж) (c/(c-1) — (c+1)/c)/(c/(c+1) — (c-1)/c).

1. а)

   $$\frac{a+\frac{1}{b}}{a-\frac{1}{b}}=\frac{\frac{ab+1}{b}}{\frac{ab-1}{b}}=\frac{ab+1}{b}\cdot\frac{b}{ab-1}=\frac{ab+1}{ab-1}.$$

2. б)

   $$\frac{m-\frac{1}{n}}{n+\frac{1}{m}}=\frac{\frac{mn-1}{n}}{\frac{mn+1}{m}}=\frac{mn-1}{n}\cdot\frac{m}{mn+1}=\frac{m(mn-1)}{n(mn+1)}.$$

3. в)

   $$\frac{\frac{1}{a}+\frac{1}{b}}{\frac{1}{a}-\frac{1}{b}}=\frac{\frac{b+a}{ab}}{\frac{b-a}{ab}}=\frac{b+a}{ab}\cdot\frac{ab}{b-a}=\frac{a+b}{b-a}.$$

4. г)

   $$\frac{\frac{a}{b}-\frac{m}{n}}{\frac{a}{b}+\frac{m}{n}}=\frac{\frac{an-bm}{bn}}{\frac{an+bm}{bn}}=\frac{an-bm}{bn}\cdot\frac{bn}{an+bm}=\frac{an-bm}{an+bm}.$$

5. д)

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

6. е)

   $$\frac{\frac{1}{1-m}+\frac{1}{1+m}}{\frac{1}{1-m}-\frac{1}{1+m}}= \frac{\frac{1+m+1-m}{(1-m)(1+m)}}{\frac{1+m-1+m}{(1-m)(1+m)}}= \frac{\frac{2}{1-m^2}}{\frac{2m}{1-m^2}}=\frac{1}{m}.$$

7. ж)

   $$\frac{\frac{c}{c-1}-\frac{c+1}{c}}{\frac{c}{c+1}-\frac{c-1}{c}}= \frac{\frac{c^2-(c+1)(c-1)}{c(c-1)}}{\frac{c^2-(c-1)(c+1)}{c(c+1)}}= \frac{\frac{c^2-(c^2-1)}{c(c-1)}}{\frac{c^2-(c^2-1)}{c(c+1)}}= \frac{\frac{1}{c(c-1)}}{\frac{1}{c(c+1)}}= \frac{c+1}{c-1}.$$

Ответ

а) $$\frac{ab+1}{ab-1}$$; б) $$\frac{m(mn-1)}{n(mn+1)}$$; в) $$\frac{a+b}{b-a}$$; г) $$\frac{an-bm}{an+bm}$$; д) $$1$$; е) $$\frac{1}{m}$$; ж) $$\frac{c+1}{c-1}$$.