aufklären
to solve
To investigate an unclear matter, a crime, or a mystery and find out the truth.
Die Polizei konnte den Diebstahl schnell aufklären.
The police were able to solve the theft quickly.

to clarify / clear up
Loading your saved state.
to solve
To investigate an unclear matter, a crime, or a mystery and find out the truth.
Die Polizei konnte den Diebstahl schnell aufklären.
The police were able to solve the theft quickly.

'Aufklären' (to clarify / clear up) is a separable verb. In a main clause, the prefix 'auf' goes at the end; in a subordinate clause, the whole verb goes at the end. In the infinitive with 'zu', 'zu' comes between the prefix and the verb.
Der Detektiv klärt den Fall schnell auf.
The detective solves the case quickly.
The verb is made up of the prefix 'auf' and the verb 'klären' (to clarify). 'Klären' means to make something clear. The prefix 'auf' reinforces this and means to make something completely clear or open.
Ein Anruf bei der Bank konnte die Verwirrung aufklären.
A call to the bank was able to clear up the confusion.
The meaning of 'aufklären' (to clarify / clear up) often depends on the grammatical structure. 'Etwas aufklären' means to solve something, 'jemanden über etwas aufklären' means to inform someone about something, 'sich aufklären' means that something becomes clear on its own, and 'es klärt auf' refers to the weather.
Die Polizei klärt ein Verbrechen auf.
The police solve a crime.
In the meaning of 'lösen' (to solve), the verb is often used with words such as 'ein Verbrechen' (a crime), 'einen Mord' (a murder), 'einen Diebstahl' (a theft), or 'ein Rätsel' (a riddle/mystery).
Die Kommissarin konnte den komplizierten Mordfall aufklären.
The detective was able to solve the complicated murder case.
When you inform someone, the topic of the information is introduced with the preposition 'über' and the accusative.
Wir müssen die Mitarbeiter über die neuen Regeln aufklären.
We have to inform the employees about the new rules.
When talking about the weather, 'aufklären' (to clear up) is often used with the impersonal pronoun 'es' as the subject.
Ich hoffe, es klärt bald wieder auf.
I hope it clears up again soon.
to explain / declare
'erklären' and 'aufklären' can both mean that something becomes clearer. 'erklären' is used when someone makes a situation, rule, or function understandable. 'aufklären' fits more when something was previously unclear, secret, or misunderstood, and then the truth or important information becomes visible. You can 'jemanden über ein Thema aufklären' (inform someone about a topic), but you would more likely 'eine Matheaufgabe erklären' (explain a math problem). Learners may confuse the words because both have to do with understanding. A good guideline is: 'erklären' helps with understanding, while 'aufklären' removes uncertainty or lack of knowledge.

Die Polizei klärt den Diebstahl im Einkaufszentrum auf.
The police solve the theft at the shopping center.
Die Trainerin erklärt der Gruppe die neue Übung Schritt für Schritt.
The trainer explains the new exercise to the group step by step.