How can you simplify these if possible?

Question

1.) (t^2-t^3) / (t^2 -2t +1)
2.) (10r) / (2t)

Answer 1

1. -t^2(t-1)/(t-1)(t-1)
-t^2/(t-1)

2. 5r/t

Answer 2

1) (t^2-t^3)/(t^2-2t+1) = t^2(1-t)/(t-1)(t-1)
= t^2/t-1

In (1), (t-1) is a common term in both the numerator and the denominator, hence it can be canceled out. Note: (1-t) and (t-1) is the same as in (1-t), it can be converted to (-t+1) >>> (t-1) =)


2) (10r)/(2t) = 5r/t

Answer 3

1) Factor out a -t^2 from the numerator this gives you

-t^2(t - 1)

then factor the trinomial in the denominator.

(t -1)(t -1)

The (t - 1) in the num and den cancel out leaving you with

-t^2/(t -1)

2) factor out a 2 in both, leaving you with

5r/t

Answer 4

1) factor
[-t^2(t - 1)]/[(t-1)(t + 1)]
cancel (t - 1)
-t^2/(t + 1)

2) 5r/t

Answer 5

t² - t³
------------- =
t² - 2t + 1

t²(t - 1)
----------- =
(t-1)(t-1)

t²/(t-1)

10r/(2t) = 5r/t