To simplify the expression (cos 2α - sin^2α) / (2sin^2α - cos^2α), we will first expand the cosine term using the double angle formula:

cos 2α = cos^2α - sin^2α

Therefore, we can rewrite the expression as:

(cos^2α - sin^2α - sin^2α) / (2sin^2α - cos^2α)
(cos^2α - 2sin^2α) / (2sin^2α - cos^2α)

Next, we can factor out a negative sign from the numerator:

-(2sin^2α - cos^2α) / (2sin^2α - cos^2α)

Finally, we can cancel out the common terms in the numerator and the denominator:

-1

Therefore, the simplified form of (cos 2α - sin^2α) / (2sin^2α - cos^2α) is -1.