Handle more than one application with one virtual server

Yeah i understand the configuration might be a lillte bit confusing, maybe there is a easier way. So let me give you the config from TMOS output:

This is the VIP:

ltm virtual vs_default-app {
    description default web app
    destination 193.xxx.xxx.xxx:https
    ip-protocol tcp
    mask 255.255.255.255
    pool pool_default-app
    profiles {
        clientssl_default-app {
            context clientside
        }
        http { }
        serverssl-insecure-compatible {
            context serverside
        }
        tcp { }
    }
    rules {
        irule_new-web-app
    }
    source 0.0.0.0/0
    source-address-translation {
        type automap
    }
    vs-index 15
}

So this VIP has the pool default-app, now we have the situation that we should deliver a new app over the same DNS alias so let's say now it's like this https://www.default-app.com is routed to the VIP and to the default-app pool.

The new app should be access via https://www.default-app.com/new-app therfore the irule that all traffic where the uri starts with /new-app is going to the second pool (pool new-app).

But here we have the problem because we only have /new-app on the first access in the uri. And therefore i want to add a persistence to this rule.

Do you know if this is working or not? Or maybe you have a not so confusing configuration idea for me.

Thanks, Christoph