To simplify this expression, we will first work on simplifying the numerator and denominator separately before combining them.
Numerator:a - a^(-3) / a - 2= a - 1/a^3 / a - 2= (a^4 - 1) / (a^3 (a - 2))= (a^2 + 1)(a + 1)(a - 1) / (a^3 (a - 2))
Denominator:3 - 2a / 4 - 4a + a= 3 - 2a / 4 - 3a= 3 - 2a / -a= -(3 - 2a) / a= (2a - 3) / a
Now, combine the numerator and denominator:((a^2 + 1)(a + 1)(a - 1)) / (a^3 (a - 2)) / ((2a - 3) / a)= ((a^2 + 1)(a + 1)(a - 1)) / (a^3 (a - 2)) (a / (2a - 3))= ((a^2 + 1)(a + 1)(a - 1) a) / (a^3 (a - 2) (2a - 3))
To simplify this expression, we will first work on simplifying the numerator and denominator separately before combining them.
Numerator:
a - a^(-3) / a - 2
= a - 1/a^3 / a - 2
= (a^4 - 1) / (a^3 (a - 2))
= (a^2 + 1)(a + 1)(a - 1) / (a^3 (a - 2))
Denominator:
3 - 2a / 4 - 4a + a
= 3 - 2a / 4 - 3a
= 3 - 2a / -a
= -(3 - 2a) / a
= (2a - 3) / a
Now, combine the numerator and denominator:
((a^2 + 1)(a + 1)(a - 1)) / (a^3 (a - 2)) / ((2a - 3) / a)
= ((a^2 + 1)(a + 1)(a - 1)) / (a^3 (a - 2)) (a / (2a - 3))
= ((a^2 + 1)(a + 1)(a - 1) a) / (a^3 (a - 2) (2a - 3))