Simplify this.. Please!?

Question

1-16/y^2
_______ 1-8/y + 16/y^2

Answer 1

Start by simplifying the numerator.
1 - 16/y²

So combine these fractions into one, use a common denominator of y²:
y²/y² - 16/y²

This becomes a single fraction of:
y² - 16
---------
... y²

Next simplify the denominator.
1 - 8/y + 16/y²

Get common denominator for all the terms of y².
y²/y² - 8y/y² + 16/y²

Now you can add them together as a single fraction:
y² - 8y + 16
---------------
..... y²

Put these two fractions over each other and the y² terms in each of their denominators will cancel out:

y² - 16
---------------
y² - 8y + 16

Now you can factor the numerator as a difference of squares:
(y - 4)(y + 4)
-----------------
y² - 8y + 16

And the denominator is a perfect square:
(y - 4)(y + 4)
-----------------
(y - 4)(y - 4)

Cancel one of the y-4 terms from top and bottom:

y + 4
-------
y - 4

Answer 2

top:
put on common denominator (in this case, y^2)

1 - 16/y^2
becomes
y^2/y^2 - 16/y^2
(y^2 - 16)/y^2
(y+4)(y-4)/y^2

Bottom

y^2/y^2 - 8y/y^2 + 16/y^2

(y^2 -8y + 16)/y^2

Inside the braquet is a square.

when you divide top by bottom the y^2 outside the brackets cancel out because anything over itself is 1 (except 0/0 which is always weird).

so (1/y^2)/(1/y^2) = 1
(Anything over itself)

you will be left with the "difference of squares" at the top and the square at the bottom.

one (y-4) will cancel out, leaving you with one 1st-degree bracket on top and one 1st-degree bracket on the bottom.

It will look cool