Question

Помогите пожалуйста сделать номер 573

Answer 1

$1) ( frac{a}{a+1}+1):(1- frac{3a^2}{1-a^2})= ( frac{a+a+1}{a+1} ):( frac{1-a^2-3a^2}{(1-a)(1+a)} ) \ = frac{2a+1}{a+1}: frac{1-4a^2}{(1-a)(1+a)}= frac{2a+1}{a+1}* frac{(1-a)(1+a)}{(1-2a)(1+2a)}= frac{1-a}{1-2a}; \ 2) ( frac{2m+1}{2m-1}- frac{2m-1}{2m+1}): frac{4m}{10m-5}=( frac{4m^2+4m+1-4m^2+4m-1}{(2m-1)(2m+1)})* frac{5(2m-1)}{4m}= \ = frac{8m}{(2m-1)(2m+1)}* frac{5(2m-1)}{4m}= frac{10}{2m+1};$
$3) ( frac{a}{x-a}+ frac{a}{x+a})* frac{x^2+2ax+a^2}{2a^2}= frac{ax+a^2+ax-a^2}{(x-a)(x+a)}* frac{(x+a)^2}{2a^2}= \ =frac{2ax}{(x-a)(x+a)}* frac{(x+a)^2}{2a^2}= frac{x(x+a)}{(x-a)*a}= frac{x^2+ax}{ax-a^2}; \ 4) ( frac{x^2}{y^2}+ frac{y}{x}):( frac{x}{y^2}- frac{1}{y} + frac{1}{x})= frac{x^3+y^3}{xy^2}: frac{x^2-xy+y^2}{xy^2}= frac{x^3+y^3}{xy^2}* frac{xy^2}{x^2-xy+y^2}= \ frac{(x+y)(x^2-xy+y^2)}{x^2-xy+y^2}=x+y.$