factoring rational expression

Hello, I want to factor the following:
1-(1/y^2)

I thought that this would be the correct answer:
1/y * (y-(1/y))

however my textbook says that this is correct:
(1-1/y) (1+1/y)

Can someone please tell me if my answer is just another way of how they did it in the second example, or am I wrong ?

Thanks

Quote:

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Originally Posted by fran1942

Hello, I want to factor the following:
1-(1/y^2)

I thought that this would be the correct answer:
1/y * (y-(1/y))

however my textbook says that this is correct:
(1-1/y) (1+1/y)

Can someone please tell me if my answer is just another way of how they did it in the second example, or am I wrong ?

Thanks

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by the Difference of Two Squares rule...

thanks kindly, but can you tell me how I am wrong with this answer:

1/y * (y-(1/y))

Thanks.

You're not wrong, it's just that rather than simplifying by removing common factors, you've made the expression more complicated.

I could write as if I wanted to, but would you class that as splitting it into its factors?