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

Re: factoring rational expression

Quote:

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

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

by the Difference of Two Squares rule...

Re: factoring rational expression

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

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

Thanks.

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