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Cut through the drywall to expose the old duct work and remove the old flex duct (Image 1). Now you can install the new aluminum flex duct. Begin by connecting the new flex duct to the old one in the ceiling (Image 2) and sealing them together with aluminum tape (Image 3).
Secure the duct every few feet with metal straps and screws between the studs.
Near the floor, create a 90-degree angle in the duct and install a metal access panel around it. This is where it will connect to the dryer. Once all the connections are made, re-install the drywall with tape and joint compound.