Der Text geht um den fortschritt der privatschulen.
And
Die Nachfrage nach studienplätzen ist gestiegen.
The relation between the two sentences is a cause-effect where the demand causes the advance.
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"privatenschulen" isn't a commonly used term in german language at all. Could you please give a reference, where you got that from. Also "Die Nachfrage nach studienplätze ist gestiegen." should rather be "Die Nachfrage nach Studienplätzen ist gestiegen." Your question is a bit unclear, consider what are your particular concerns please. – πάντα ῥεῖ Apr 17 '18 at 19:51
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3How are we supposed to know what the relation between the two sentences is? – Carsten S Apr 17 '18 at 20:32
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1So the demand caused the text? Or the other way around? Or did the progress cause the demand? – Carsten S Apr 17 '18 at 20:35
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1Take into account that there is absolutely no relationship in the German educational system between "Privatschulen" and "Studienplätzen". This might cause the confusion of many people. – tofro Apr 17 '18 at 21:02
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1The above is a comment, not an answer. And comments, are, well, for commenting. – tofro Apr 17 '18 at 21:08
A rather simple way to connect:
In dem Text geht es um den Aufschwung der Privatschulen infolge der gestiegenen Nachfrage nach Studienplätzen.
In dem Text geht es um die Belebung der Privatschulen infolge der gestiegenen Nachfrage nach Studienplätzen.
Der Text geht um den fortschritt der privatenschulen.In dem Text geht es um die Ausbreitung der/von Privatschulen.
Die Nachfrage nach Studienplätzen ist gestiegen.
I assume the second sentence is giving the reason for the first.
In dem Text geht es um die wegen der gestiegenen Nachfrage nach Studienplätzen stattfindenden Ausbreitung der/von Privatschulen.
Stattfindenden is the Partizip I of the verb stattfinden. This participle is used for inserts that give a simultaneous or concurrent action. In combination with wegen it creates a Klammer around a reason.
Instead of stattfinden, you can also use other verbs, e.g. geschehen, passieren, even explodieren, if you want to say private schools literally boom.
It's okay, even more natural to use von+Dativ instead of der+Genitiv in this sentence, as Privatschulen is a kind of thing here, not a particular thing.
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