Wiedząc że [latex] frac{x+2y}{x-2y} =7[/latex], oblicz [latex] frac{x+3y}{x-3y}[/latex] Pozdrawiam

[latex]frac{x+2y}{x-2y}=frac{x-2y+4y}{x-2y}=1+frac{4y}{x-2y}\ frac{x+3y}{x-3y}=frac{x-3y+6y}{x-3y}=1+frac{6y}{x-3y}\ 1+frac{4y}{x-2y}=7\ frac{4y}{x-2y}=6\ 4y=6x-12y\ 6x=16y\ x=frac{8}{3}y\ x-3y=frac{8}{3}y-3y=-frac{1}{3}y\ frac{6y}{-1/3y}=frac{6y}{1}*frac{-3}{y}=-18\ 1-18=-17[/latex]

[latex]frac{x+2y}{x-2y} = 7\\7(x-2y) = x+2y\\7x-14y = x+2y\\6x = 16y /:6\\x = frac{8y}{3}[/latex] [latex]frac{x+3y}{x-3y} = frac{ frac{8y}{3}+3y}{frac{8y}{3}-3y}}\\frac{x+3y}{x-3y} = frac{frac{17y}{3}}{frac{-y}{3}}\\frac{x+3y}{x-3y} = -17[/latex]