SOLUTION: Have I simplified the below problem corectly? 16x^2 -1 over Y^2 divided by 4x + 1 over y^3 = 4xy Thank you

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Question 1169452: Have I simplified the below problem corectly?
16x^2 -1 over Y^2 divided by 4x + 1 over y^3 = 4xy
Thank you
Found 2 solutions by Edwin McCravy, Theo:
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!

Not quite. You lost a term.

%2816x%5E2-1%29%2Fy%5E2%28%22%22%2A%22%22%29%2F%28%22%22%2A%22%22%29%284x%5E%22%22+%2B+1%29%2Fy%5E3

Invert the second fraction and change division to multiplication:

%2816x%5E2-1%29%2Fy%5E2%22%22%2A%22%22y%5E3%2F%284x%5E%22%22+%2B+1%29

%28%284x%5E%22%22-1%29%284x%5E%22%22%2B1%29%29%2Fy%5E2%22%22%2A%22%22y%5E3%2F%284x%5E%22%22+%2B+1%29

%28%284x%5E%22%22-1%29%28cross%284x%5E%22%22%2B1%29%29%29%2Fy%5E2%22%22%2A%22%22y%5E3%2F%28cross%284x%5E%22%22+%2B+1%29%29

%284x%5E%22%22-1%29%2Fy%5E2%22%22%2A%22%22y%5E3%2F1

%284x-1%29y

4xy-y

Edwin

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
let me see ....

(16x^2-1)/(y^2) / (4x+1)/y^3) is equal to .....

(16x^2-1)/(y^2) * (y^3)/(4x+1) which is equal to .....

(4x-1)*(4x+1)/y^2 * (y^3)/(4x+1) which is equal to .....

y^3/y^2 * (4x-1)*(4x+1)/(4x+1).

y^3/y^2 = y
(4x+1)/(4x+1) = 1

equation becomes:

y * (4x-1) 4xy - y.

you seem to be missing a y somewhere.

to confirm, let y = a random value and x = a random value.
i chose y = 7 and x = 3

((16x^2-1)/y^2) / ((4x+1)/y^3) = 77

4xy = 84

4xy-y = 77

this is easier to see what happens on a manually derived worksheet.

here's my worksheet.