Question

1)$frac{y^{2} }{x-xy} : ( frac{y}{x-y}- frac{2xy}{ x^{2} - y^{2} } )$

2)$frac{25 n^{2}-b^{2} }{25 a^{2}-10ab+b^{2}}:(5 a^{2}+ab ) *(2b-10a)$

При а=25,в=56

Answer 1

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

2) Мне кажется в первом числителе 25a. а не 25n
$frac{25a^2-b^2}{25a^2-10ab+b^2}:(5a^2+ab)*(2b-10a)= \ frac{(5a)^2-b^2}{(5a)^2-2*5ab+b^2}* frac{1}{a(5a+b)}*2(b-5a)= \ frac{(5a+b)(5a-b)}{(5a-b)^2}* frac{1}{a(5a+b)}*(-2)(5a-b)= \ frac{(5a+b)(5a-b)}{(5a-b)}* frac{1}{a(5a+b)}*(-2)=frac{(5a+b)(5a-b)}{(5a-b)}* frac{1}{a(5a+b)}*(-2)= \ =frac{(5a-b)}{(5a-b)}* frac{1}{a}*(-2)=frac{1}{1}* frac{1}{a}*(-2)=-2/a$