Learn English – contraction for “where are” like “where’s” for “where is”

If you wish to rewrite a sentence containing a contraction in a way that does not use the contraction, start with replacing the contraction with the phrase it contracts.

She can't find her keys.

This would become:

She cannot find her keys.

This sentence looks fine as it is. If the sentence looks good, there is no need to do more.

Sometimes, though, a sentence rewritten in this way won't read quite right. The example used in the question is a good one.

Why can't we use this to do that?

If we replace the contraction here, we get:

Why cannot we use this to do that?

What's happening here is that the word "not", which is an adverb, is separated from the verb it modifies. Start by splitting "cannot" up into its two contained words ("can" and "not"), then use your normal understanding of English sentence structure to move the word "not" to where it needs to be to modify the verb.

Why can not we use this to do that?

This becomes:

Why can we not use this to do that?

And there you are. The adverb is in the right place now.