Which pair of words share the same prefix?

competent and correspondent

impatient and incomplete

nuisance and tolerance

disintegrate and disappear

The words that share the same prefix are disintegrate and disappear.

Prefixes are letters that are inserted before a word to change its meaning. By adding a prefix, the original word can have an opposite meaning or express a relation of time, manner or place. In this case, the prefix dis - has the meaning of remove or reverse.

Disintegrate and disappear because they both start with Dis