Question 949097

(t/t+1)^2-(t/t+1)-12=0
<pre>{{{(t/(t + 1))^2 - (t/(t + 1)) - 12 = 0}}}
Let a = {{{(t/(t + 1))}}}
Then {{{(t/(t + 1))^2 - (t/(t + 1)) - 12 = 0}}} becomes: {{{a^2 - a - 12 = 0}}}
(a - 4)(a + 3) = 0
a - 4 = 0           OR           a + 3 = 0
a = 4               OR           a = - 3

{{{4 = (t/(t + 1))}}} ------- Substituting 4 for a
4(t + 1) = t ------ Cross-multiplying
4t + 4 = t
4t - t = - 4
3t = - 4
{{{highlight_green(t = - 4/3)}}}

{{{- 3 = (t/(t + 1))}}} ------- Substituting - 3 for a
- 3(t + 1) = t ----- Cross-multiplying
- 3t - 3 = t
- 3t - t = 3
- 4t = 3
{{{highlight_green(t = - 3/4)}}}