Question

помгите желательно на листочке плииз

Answer 1

$( frac{x}{x+1} +1) * frac{1+x}{2x-1} = frac{x+x+1}{x+1} * frac{x+1}{2x-1} = frac{2x+1}{x+1} * frac{x+1}{2x-1} = frac{2x+1}{2x-1}$



$(frac{4y}{2-y} -y) : frac{y+2}{y-2} = frac{4y-y(2-y)}{2-y} : frac{y+2}{y-2}= frac{4y-2y+y^2}{2-y} * frac{y-2}{y+2} = \ \ = frac{2y+y^2}{-1(y-2) } * frac{y-2}{y+2} = frac{y(y+2)}{-1} * frac{1}{y+2} = frac{y}{-1} =-y$



$frac{a+3}{a^2+9} * ( frac{a+3}{a-3} + frac{a-3}{a+3} ) = frac{a+3}{a^2+9} * ( frac{(a+3)(a+3)+(a-3)(a-3)}{(a-3)(a+3)} ) = \ \ = frac{a+3}{a^2+9} * frac{a^2+6a+9+a^2-6a+9}{(a-3)(a+3)} = frac{(a+3)(2a^2+18)}{(a^2+9)(a-3)(a+3)} = \ \ =frac{1*(2a^2+18)}{(a^2+9)(a-3)} = frac{2(a^2+9)}{(a^2+9)(a-3)} = frac{2}{a-3}$


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