Sentence Analysis--Infinitives & Participles

a) I should write it this way to keep it easy to read, while to keep it formal.

The above is clearly not grammatical. It needs to be this:

b) I should write it this way to keep it easy to read, and to keep it formal.

1) Why can't 'while' join two infinitive phrases?





2) This one below seems right. Why can 'while' join an infintive to an ing (but not to another infinitive)?

c) I should write it this way to keep it easy to read, while keeping it formal.







Thanks