Help for an Old and Frayed Cable Outlet

There are two cable outlets that connect to my unit. One was used to install my chromebook with no difficulty. I want to hook up a new TV with cable but the other cable looks frayed and as if it would not hold. I have not the first idea about how to address this. I find it hard to believe I am the first in the history of home installations to face this issue. Can I 'add on' to the working outlet? Is there a way to update the old one or create a bridge? Any help would be very much appreciated.

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Clarification Request
Without knowing the exact cable and connector type?

Sorry no. It's a job for an electrician until more is known.

The forum supports pictures so take a snap, make it good and clear, put it on imgur and use the new forum feature. for example walks us through putting one type connector on a wire.

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Youtube and other forums have DIY specifics on this stuff

If you want to get your feet wet with repairing the outlet, that's where I might start.

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