2008 trail blazer 4.2 4x4 fan under the hood runs all the time. Why how to fix?

You probably mean your fan clutch. Always engaged, unfortunately it's a very common problem with our platform. Replace your fan clutch.

What fan ? Your vehicle doesn't electric cooling fans , has engine cooling fan and clutch driven by the crankshaft via the drive belt. Your probably taking about the
Secondary Air Injection System Description .
The secondary air injection (AIR) system aids in the reduction of hydrocarbon exhaust emissions during a cold start-up. This occurs when the start-up engine coolant temperature (ECT) is between 5-50?°C (41-122?°F), and the intake air temperature (IAT) is between 5-60?°C (41-140?°F). The AIR pump operates 5-60 seconds after start-up.
The engine control module (ECM) activates the AIR system by simultaneously supplying grounds to the AIR pump and the AIR valve relays. This action closes the relays' internal contacts. The AIR pump and the AIR control solenoid valve/pressure sensor assembly are in turn energized, the pump runs and the control/shut-off valve opens.
The AIR pump sends pressurized fresh air into the pipes/hoses through the open control/shut-off valve, and into the exhaust manifold. The extra air accelerates the catalyst operation, helping it to reach operating temperature faster. The AIR pump remains ON for a short period of time after the control/shut-off valve is commanded OFF. When the AIR pump is commanded OFF it will not run or be activated until the next vehicle start. When the AIR system is inactive, the closed AIR control/shut-off valve prevents air/exhaust flow in either direction.
In the under hood fuse box find AIR PUMP fuse # 64 60amp pull the fuse an see if the fan goes off . There are two relays secondary Air injection (AIR ) pump relay . The contacts may be stuck together .
In the under