verkraften
to cope with
To cope with and process a difficult emotional or psychological situation.
Es hat lange gedauert, bis sie die Trennung verkraftet hat.
It took a long time before she coped with the breakup.

to cope with / withstand
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to cope with
To cope with and process a difficult emotional or psychological situation.
Es hat lange gedauert, bis sie die Trennung verkraftet hat.
It took a long time before she coped with the breakup.

'Verkraften' (to cope with / withstand) is an inseparable verb. The prefix 'ver-' remains firmly attached to the verb in all sentence forms and is not placed at the end of the sentence.
Ich hoffe, er verkraftet die schlechte Nachricht gut.
I hope he copes with the bad news well.
The word contains the stem 'Kraft' (strength). 'Verkraften' (to cope with / withstand) therefore means to muster the necessary emotional, financial, or physical strength to deal with a burden.
Sie musste all ihre Kraft aufwenden, um den Verlust zu verkraften.
She had to use all her strength to cope with the loss.
'Verkraften' (to cope with / withstand) is a transitive verb and always requires an accusative object. You always cope with or withstand 'etwas' (something).
Die Firma konnte den finanziellen Schaden nicht verkraften.
The company could not withstand the financial damage.
The context makes clear what kind of burden is meant. Emotional events such as a shock or disappointment, financial burdens such as costs or losses, or physical strain such as an illness or training determine the exact meaning.
Er konnte die Kritik an seiner Arbeit nur schwer verkraften.
He found it hard to cope with the criticism of his work.
to wear / carry
'tragen' and 'verkraften' can both be used with burdens or strains. Here, 'tragen' means that someone bears responsibility, costs, or consequences. 'verkraften' means that someone withstands and copes with a difficult situation, a financial burden, or physical exertion. So you can bear the costs, but you have to cope with the loss or the stress. The words are easy to confuse because both show that something is difficult for a person.

Nach der langen Krankheit muss Mehmet erst wieder lernen, Belastung zu verkraften.
After the long illness, Mehmet first has to learn to withstand physical strain again.
Die Firma trägt die Kosten für die Reise.
The company bears the cost of the trip.