SOLUTION: t+10 / 7-t = 3 / t-7

Algebra ->  Systems-of-equations -> SOLUTION: t+10 / 7-t = 3 / t-7      Log On


   

Question 21944: t+10 / 7-t = 3 / t-7
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
first cross-multiply (multiply both sides by 7-t, then multiply both sides by t-7)
(t + 10)(t - 7) = 3(7 - t)
t^2 + 3t - 70 = 3(7 - t)
expanding
t^2 + 3t - 70 = 21 - 3t
expanding
t^2 +6t -91 = 0
adding 3t to both sides and subtracting 21 from both sides
use the quadratic formula:
%28-b+%2B-sqrt%28b%5E2+-+4ac%29%29%2F2a
you will get:
%28-6+%2B-sqrt%2836+-+4%2A%28-91%29%29%29%2F2%29
%28-6+%2B-+20%29+%2F2
-3+%2B-+10
7, -13
if you substitute 7 into the original equation, you get 7 - 7 in both denominators. this says infinity = infinity.
if you substitute -13 into the original equation, you get:
%28-3%29+%2F+20+=+3+%2F+%28-20%29
the solutions check ok