Question

Find any excluded values of each rational expression.

1. t - 1/ t^2 - t

A: Excluded value: 1.

Simplify each rational expression, if possible. Identify any excluded values.

2. 3x^2/6x^3

A: 2x; x ≠ 2

3. 2n/n^2 - 3n

A: ?

4. s + 1/s^2 - 4s - 5

A: ?

5. 12 - 3x/x^2 - 8x + 16

A: ?

Answer 1

#1 also t=0, since t^2-t = t(t-1)
The original expression must be examined for excluded values.
(t-1)/(t^2-t) = 1/t, so t≠0. But dividing top and bottom by t-1 to get there means that t≠1, because you cannot divide by zero.

#2 huh? There is no x-2 in the denominator.

1/(2x) x≠0

#3
2n / n(n-3) = 2/(n-3), x≠0,3
Same as #1 for logic.

#4
(s+1) / (s+1)(s-5)
s≠-1,5

#5
3(4-x) / (x-4)^2 = -3/(x-4), x≠4