Question

Решите эти три , сделаю ответ лучшим

Answer 1

1A005

$1)\frac{m+1}{m} -\frac{1}{m-m^{2}}=\frac{m+1}{m}-\frac{1}{m(1-m)}=\frac{1-m^{2}-1 }{m(1-m)}=-\frac{m^{2}}{m(1-m)}=\frac{m}{m-1}\\\\2)(m-\frac{m^{2}}{m-1})^{-1}=(\frac{m^{2}-m-m^{2}}{m-1})^{-1} =(\frac{m}{1-m})^{-1}=\frac{1-m}{m}\\\\3)\frac{m}{m-1}*\frac{1-m}{m}=-1\\\\4)4*(-1)=-4Otvet:\boxed{-4}$

1A006

$1)\frac{(a^{2}-b^{2})(a^{2}+ab+b^{2})}{b^{3}-\frac{a^{3}+b^{3}}{2}}=\frac{(a+b)(a-b)(a^{2}+ab+b^{2})}{\frac{2b^{3}-a^{3}-b^{3}}{2}}=\frac{2(a+b)(a^{3}-b^{3})}{b^{3}-a^{3}}=-2(a+b)\\\\2)-2(a+b)*\frac{1}{a+b}=-\frac{2(a+b)}{a+b}=-2\\\\Otvet:\boxed{-2}$

1A007

$1)\frac{2xy}{y^{2}-x^{2}}+\frac{x}{x+y}-\frac{y}{y-x}=\frac{2xy}{(y-x)(y+x)}+\frac{x}{x+y}-\frac{y}{y-x}=\frac{2xy+xy-x^{2}-y^{2}-xy}{(y-x)(y+x)} =\frac{-x^{2}+2xy-y^{2}}{(y-x)(y+x)}=-\frac{x^{2}-2xy+y^{2}}{(y-x)(y+x)}=-\frac{(x-y)^{2}}{(y-x)(y+x)}=\frac{x-y}{x+y}\\\\2)\frac{y-x}{x+y}:\frac{x-y}{x+y}=\frac{y-x}{x+y}*\frac{x+y}{x-y}=-1\\\\Otvet:\boxed{-1}$