Question

299 пожалуйста помогите мне

Answer 1

1) $(2x-y- frac{2x-y^2}{y} )* frac{a}{3xy-3x}- frac{a-1}{y} =$
$=frac{2xy-y^2-2x+y^2}{y}* frac{a}{3xy-3x}- frac{a-1}{y} =frac{2xy-2x}{y}* frac{a}{3xy-3x}- frac{a-1}{y}=$
$=frac{2(xy-x)}{y}* frac{a}{3(xy-x)}- frac{a-1}{y}=frac{2a}{3y}- frac{a-1}{y}=frac{2a}{3y}- frac{3a-3}{3y}= frac{3-a}{3y}$

2) $frac{a}{a^2-2a+1}- frac{1}{1-a}* frac{a}{a+1} - frac{2}{a+1} = frac{a}{(a-1)^2}+ frac{1}{a-1}* frac{a}{a+1} - frac{2}{a+1} =$
$=frac{a(a+1)}{(a-1)^2(a+1)}+ frac{a(a-1)}{(a-1)^2(a+1)} - frac{2(a-1)^2}{(a-1)^2(a+1)} =$
$=frac{a^2+a+a^2-a-2(a^2-2a+1)}{(a-1)^2(a+1)}=frac{2a^2-2a^2+4a-2}{(a-1)^2(a+1)}=frac{4a-2}{(a-1)^2(a+1)}$

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

4) $( frac{m}{n^2+mn} - frac{m-n}{m^2+mn} ):( frac{n^2}{m^3-mn^2} + frac{1}{m+n} )=$
$=( frac{m}{n(n+m)} - frac{m-n}{m(m+n)} ):( frac{n^2}{m(m^2-n^2)} + frac{1}{m+n} )=$
$=( frac{m^2}{mn(m+n)} - frac{mn-n^2}{mn(m+n)} ):( frac{n^2}{m(m-n)(m+n)} + frac{m(m-n)}{m(m-n)(m+n)} )=$
$=frac{m^2-mn+n^2}{mn(m+n)}:frac{n^2+m^2-mn}{m(m-n)(m+n)}=frac{m^2-mn+n^2}{mn(m+n)}* frac{m(m-n)(m+n)}{n^2+m^2-mn}= frac{m-n}{n}$