Question 369941
{{{(z)/(-6)=(x+y)/(x-y)}}} Start with the given equation.



{{{z(x-y)=-6(x+y)}}} Cross multiply



{{{zx-zy=-6x-6y}}} Distribute.



{{{zx-zy+6x=-6y}}} Add 6x to both sides.



{{{zx+6x=-6y+zy}}} Add zy to both sides.



{{{x(z+6)=y(-6+z)}}} Factor out the GCF 'x' from the left side. Factor out the GCF 'y' from the right side.



{{{(x(z+6))/y=-6+z}}} Divide both sides by 'y'.



{{{x/y=(-6+z)/(z+6)}}} Divide both sides by {{{z+6}}}.



{{{x/y=(z-6)/(z+6)}}} Rearrange the terms.



So the ratio of x to y is {{{(z-6)/(z+6)}}} 



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