Question on factoring binomials with fractions?

Question

Factor the binomial

1/49 - x^2

I rearranged the problem and then got rid of the negative sign

x^2 - 1/49

Then I think I need to switch the denominator and numerator to make it a positive so I get

x^2 + 1/49

And Im not sure how to factor that. Sorry if none of my steps make sense, I am not good with fractions.

Answer 1

well you can't rearrange that problem like that. Here:
1/49-x^2
(1/7+x)(1/7-x)
then, when you multiplty them to check, it turns out:
(1/7+x) * (1/7-x)= 1/49+1/7x-1/7x-x^2
the 1/7x cancels out so the final answer is :
(1/7+x)(1/7-x)

Answer 2

You can rearrange the problem this way but you can do it as written

1/49-x^2 is simply a perfect square witten differently

(1/7-x)(1/7 +x) gives you the desired result