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

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) (Show Source): You can put this solution on YOUR website!
Start with the given expression.

Factor a -1 from the numerator.

Factor a -1 from the denominator.

Rearrange the terms.

Reduce. In other words, simplify to get 1 (which is then absorbed into the expression).

So where
Answer by JimboP1977(311) (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

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