Question

simplify each complex fraction t - t^-2 / 1 - t^-1

Answer 1

t^-2 =1/(t^2), etc.

rewrite the problem according to this, then simplify.

Answer 2

Multiply EVERY term by t^2 to get (t^3-1)/(t^2-t). Then factor and simplify if possible.

Answer 3

is the answer(t^2 + t +1)/t ?

Answer 4

(t-t^-2)/(1-t^-1)
(t-1/t^2)/(1-1/t)
[(t^3-1)/t^2]/[(t-1)/t]
[(t^3-1)/t^2][t/t-1]
[(t-1)(t^2+t+1)/t^2][t/t-1]
(t^2+t+1)/t

Answer 5

t^3-1 = (t-1)(t^2+t+1) and t^2-t = t(t-1). Notice that these two factorizations share a "t-1" term in common. So they cancel out. This means that the whole fraction simplifies to (t^2 + t +1)/t, so you are correct. Good job.

Answer 6

aftrcal1's answer is the correct one