SOLUTION: While I can solve for y, I believe I'm missing something with the absolute value sign. There are pipes on the left side of the equation around the whole fraction. I think it change

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Question 1127709: While I can solve for y, I believe I'm missing something with the absolute value sign. There are pipes on the left side of the equation around the whole fraction. I think it changes the whole solution. Can someone elaborate please?
| +%282y%29%2F%28y%5E2+-1%29+ | = 2
Found 2 solutions by MathLover1, Boreal:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

+abs%282y%2F%28y%5E2+-1%29%29++=+2
+2abs%28y%2F%28y%5E2+-1%29%29++=+2
+abs%28y%2F%28y%5E2+-1%29%29++=+2%2F2
+abs%28y%2F%28y%5E2+-1%29%29++=+1
solutions: since abs value of the +y%2F%28y%5E2+-1%29+ and +-%28y%2F%28y%5E2+-1%29%29+ is same, we have
+y%2F%28y%5E2+-1%29++=+1 or +-y%2F%28y%5E2+-1%29++=+1

1.
+y%2F%28y%5E2+-1%29++=+1
+y++=+y%5E2+-1
++y%5E2-y+-1=0
%28y+-+1%2F2%29%5E2+-+1%2F4-1+=+0
++%28y-1%2F2%29%5E2-5%2F4=0
++%28y-1%2F2%29%5E2=5%2F4
++%28y-1%2F2%29=sqrt%285%2F4%29
++y=1%2F2%2B+sqrt%285%29%2F2
++y=%281%2F2%29%281%2B+sqrt%285%29%29 or ++y=%281%2F2%29%281-+sqrt%285%29%29





Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
The absolute value symbol is | |, a bracket. This is an absolute value problem where everything in the bracket is computed and then the positive value only is used. |-2|=|2|=2
2y/(y^2-1)=2
2y=2y^2-2
2y^2-2y-2=0
y^2-y-1=0
y=(1/2)(1+/-sqrt(5))
numerical is 1.618, -0.568
2y/(y^2-1)=-2
2y=-2y^2+2
2y^2+2y-2=0
y^2+y-1=0
y=(1/2)(-1+/- sqrt(5))
numerical is -1.618, 0.568
graph shows answers on the x-intercept
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cabs%282x%2F%28x%5E2-1%29%29-2%29