Hello, leviathanwave!

Here are some of them . . .

Factor: .

For is always positive.

Hence: must be positive.

We have: .

Solution: .

The numerator is already negative.

For the fraction to be positive, its denominator must also be negative.

We have: .

Solution: .

This is a messy one . . . I'll let someone else explain it.

We have: .

Solution: .