SOLUTION: 8-y/2-y=y-8/y-2 I know these are equal. But why??? I have to prove why they are equal. I was thinking maybe if I multiply them by their inverses then they would both equal 1. Plea

Algebra ->  Equations -> SOLUTION: 8-y/2-y=y-8/y-2 I know these are equal. But why??? I have to prove why they are equal. I was thinking maybe if I multiply them by their inverses then they would both equal 1. Plea      Log On


   

Question 236455: 8-y/2-y=y-8/y-2 I know these are equal. But why??? I have to prove why they are equal. I was thinking maybe if I multiply them by their inverses then they would both equal 1. Please help.
Found 2 solutions by jim_thompson5910, JimboP1977:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%288-y%29%2F%282-y%29 Start with the given expression.


%28-%28-8%2By%29%29%2F%282-y%29 Factor a -1 from the numerator.


%28-%28-8%2By%29%29%2F%28-%28-2%2By%29%29 Factor a -1 from the denominator.


%28-%28y-8%29%29%2F%28-%28y-2%29%29 Rearrange the terms.


%28y-8%29%2F%28y-2%29 Reduce. In other words, simplify -1%2F-1 to get 1 (which is then absorbed into the expression).


So %288-y%29%2F%282-y%29=%28y-8%29%2F%28y-2%29 where y%3C%3E2

Answer by JimboP1977(311) About Me  (Show Source):
You can put this solution on YOUR website!
Multiply each side by its denominator to give:
(8-y)(y-2) = (y-8)(2-y)
Multiplying the brackets gives:
8y-16-y^2+2y = 2y-y^2-16+8y
-y^2+10y-16 = -y^2+10y-16