Math Help - factoring rational expression

1. 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

2. Re: factoring rational expression

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
\displaystyle \begin{align*} 1 - \frac{1}{y^2} &= 1^2 - \left(\frac{1}{y}\right)^2 \\ &= \left(1 - \frac{1}{y}\right)\left(1 + \frac{1}{y}\right) \end{align*}

by the Difference of Two Squares rule...

3. Re: factoring rational expression

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

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

Thanks.

4. Re: factoring rational expression

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 $3x+5$ as $\frac{x^2}{94}(\frac{282}{x}+\frac{470}{x^2})$ if I wanted to, but would you class that as splitting it into its factors?