
umgehen mit
to deal with
The way one treats someone or something or copes with a situation. This verb is separable (e.g., 'er geht damit um' — he deals with it).
Er kann gut mit schwierigen Kunden umgehen.
He can deal well with difficult customers.
to handle / avoid / circulate
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to deal with
The way one treats someone or something or copes with a situation. This verb is separable (e.g., 'er geht damit um' — he deals with it).
Er kann gut mit schwierigen Kunden umgehen.
He can deal well with difficult customers.

to avoid
To avoid something (a rule, a problem, an obstacle) by finding a way around it. This verb is inseparable (e.g., 'er umgeht das Problem' — he avoids the problem).
Er versucht, die neuen Steuervorschriften geschickt zu umgehen.
He is trying to cleverly avoid the new tax regulations.

to circulate
To spread; to be in circulation. Often used for rumors or illnesses. This verb is separable (e.g., 'ein Gerücht geht um' — a rumor is circulating).
Es geht das Gerücht um, dass die Firma verkauft werden soll.
There is a rumor circulating that the company is going to be sold.

to toy with
To have plans or intentions to do something specific. This verb is reflexive and separable (e.g., 'er geht sich mit dem Gedanken um' — he is toying with the idea).
Sie geht sich schon lange mit dem Gedanken um, auszuwandern.
She has long been toying with the idea of emigrating.
This verb is difficult because it is separable or inseparable depending on the meaning. Separable ('mit etwas umgehen' — to deal with something) means 'to handle'. Inseparable ('etwas umgehen' — to avoid something) means 'to avoid' or 'to bypass'.
Sie geht professionell mit der Kritik um.
She deals with the criticism professionally.
In the meaning 'to handle', the verb is separable and needs the preposition 'mit' followed by the dative. In a main clause, the prefix 'um' goes at the end.
Wie gehst du mit so viel Stress um?
How do you deal with so much stress?
In the meaning 'to avoid', the verb is inseparable and needs an accusative object. The prefix 'um-' is not separated from the verb.
Manche Firmen versuchen, die Steuern zu umgehen.
Some companies try to avoid taxes.
In the meaning 'to spread', the verb is separable. The subject is often impersonal, such as 'ein Gerücht' (a rumor) or 'die Angst' (fear). A typical form is 'es geht ... um' (there is ... going around).
Im Dorf geht die Angst vor dem Wolf um.
Fear of the wolf is going around in the village.
to treat / to deal with
Behandeln and umgehen mit can both describe behavior toward a person or thing. Behandeln focuses directly on the person or thing, while umgehen mit emphasizes the manner of behaving and is formed with „mit“.

Die Pflegerin geht auch unter Zeitdruck geduldig mit dem neuen Bewohner um.
The nurse deals patiently with the new resident even under time pressure.
Die Pflegerin behandelt den neuen Bewohner auch unter Zeitdruck geduldig.
The nurse treats the new resident patiently even under time pressure.