Share phone wifi with tablet

[sitlet]

OK, so I have been using my phone to tether to devices for years, so I understand how tethering works. I have a different tethering question that I haven't been able to figure out.

I just got a cheapo android tablet, works great for what I use it for. However, the wifi performance sucks. I struggle to get 5mpbs download with it. Now, my current and older android phone get great signal on WiFi. So I'm trying to figure out, without rooting, is there a way to share the wifi signal on my current or old phone, with this tablet? I know I can use bluetooth, but that's too slow to really do anything with. I'm open for anything with wifi or even a USB connection.

There's obviously tons of hotspot apps to share the phones 4g connection, but I can't seem to find anything to make the phone into say a wireless extender.

 

[ManiacJoe]

What are the radio specs on your home wifi?
What are the radio specs on your tablet's wifi?

 

[sitlet]

It's a rental modem from my cable company, not sure of the specs, but it's set to the highest power.

As for the tablet, it's a very cheap Chinese tablet and is known for bad wifi signal. I've known this going in, which is why I assumed there would be a way to tether the wifi from my phone. I can buy a WiFi extender if need be, just trying to figure out if there's a way to do this solution.