How do u simplify this fraction?

Question

How do u simplify this? z^3 – 3z^2 + z -3 / z^4 - 1

Answer 1

The key is factoring both the numerator and denominator.

Factor Numerator:
z^3 - 3z^2 + z - 3 = (z - 3) (z^2 + 1)

Factor Denominator:
z^4 -1 = (z + 1) (z - 1) (z^2 + 1)

The (z^2 + 1) cancels, leaving:
(z - 3) / (z + 1) (z - 1)

* Note in previous answers, the denominator wasn't fully factored. *
(z^2-1) = (z +1) (z - 1)

Practice your factoring skills.
Factor. Factor. Factor.
Practice. Practice. Practice.

Answer 2

You simply factor numerator and denominator separately and then cancel:

z^3 - 3z^2 + z - 3 = (z^2 + 1)(z - 3)
z^4 - 1 = (z^2 + 1)(z^2 - 1)

The (z^2 +1)'s cancel, leaving you with (z-3) / (z^2 - 1)

Answer 3

even though it's not in the problem, use some parentheses around the numerator and denominator. Which one is it?

z^3 – 3z^2 + (z -3) /( z^4) - 1

z^3 – 3z^2 + (z -3) /( z^4 - 1)

z^3 – 3z^2 + z -((3) /( z^4 - 1))

z^3 – 3z^2 + z -(3) /( z^4) - 1

Answer 4

first you factor the top of the fraction into (z^2+1)(z-3) and then you factor the bottom into (z^2+1)(z^2-1). Since there is a common term in both the top and bottom, cancel out both of the (z^2+1) and your fraction is simplified.

Answer 5

Why oh why do u have 2 ask it during the summer? I might have a better chance if u ask it in 2 weeks.

Answer 6

Have I been out of school so long that I don't remember them using" ^" ? Man, I cannot help you! Sorry!