Question

Решите пожалуйста
Сроооооооооооооооооочно

Answer 1

$3)\; \; (p+1-\frac{1}{1-p}):(p-\frac{p^2}{p-1})=\frac{(p+1)(1-p)-1}{1-p}:\frac{p(p-1)-p^2}{p-1}=\\\\=\frac{1-p^2-1}{-(p-1)}\cdot \frac{p-1}{p^2-p-p^2}=\frac{p^2}{p-1}\cdot \frac{p-1}{-p}=-p$

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

Answer 2

3)

$(p +1-\frac{1}{1-p} ):(p-\frac{p^2}{p-1} )=(p +1+\frac{1}{p-1} ):(p-\frac{p^2}{p-1} )= \frac{(p+1)(p-1)+1}{p-1} :\frac{p(p-1)-p^2}{p-1} =\\ =\frac{p^2-1+1}{p-1}* \frac{p-1}{p^2-p-p^2}= \frac{p^2}{p-1} *(-\frac{p-1}{p} )=-p$

4)

$\frac{b}{a-b}- \frac{a^3-ab^2}{a^2+b^2}*(\frac{a}{(a-b)^2} -\frac{b}{a^2-b^2}) =\frac{b}{a-b}- \frac{a(a^2-b^2)}{a^2+b^2}*(\frac{a}{(a-b)^2} -\frac{b}{(a-b)(a+b)})=\\ = \frac{b}{a-b}- \frac{a(a^2-b^2)}{a^2+b^2}*\frac{a(a+b)-b(a-b)}{(a-b)(a-b)(a+b)} =\frac{b}{a-b}- \frac{a(a^2-b^2)}{a^2+b^2}*\frac{a^2+ab-ab+b^2}{(a^2-b^2)(a-b)} =$

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