To simplify this expression, we can use the trigonometric identity:

cos(3a) = 4cos^3(a) - 3cos(a)

Therefore, the expression becomes:

(4cos^3(a) - 3cos(a) - cos(a)) / (4cos^3(a) - 3cos(a) + cos(a))

Now, we can combine like terms:

(4cos^3(a) - 4cos(a)) / (4cos^3(a) - 2cos(a))

Factor out a 4 from the numerator:

4(cos^3(a) - cos(a)) / (4cos^3(a) - 2cos(a))

Factor out a cos(a) from the denominator:

4(cos^3(a) - cos(a)) / (cos(a)(4cos^2(a) - 2))

Simplify by canceling out common terms:

4(cos^2(a) - 1) / (2cos^2(a) - 1)

Therefore, the simplified expression is:

4(cos^2(a) - 1) / (2cos^2(a) - 1)