SOLUTION: t-1/t+4 = t-7/t+5 + 1

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Question 156133: t-1/t+4 = t-7/t+5 + 1
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
%28t-1%29%2F%28t%2B4%29+=+%28t-7%29%2F%28t%2B5%29+%2B+1
Get rid of the denominators and simplify.

%28t-1%29%28t%2B5%29+=+%28t-7%29%28t%2B4%29%2B+%28t%2B4%29%28t%2B5%29
%28t%5E2%2B4t-5%29+=+%28t%5E2-3t-28%29%2B+%28t%5E2%2B9t%2B20%29
t%5E2%2B4t-5+=+2t%5E2%2B6t-8
t%5E2%2B2t-3=0
Factor the quadratic.
%28t%2B3%29%28t-1%29=0
Two solutions : t=-3,1
Check your answer.
%28t-1%29%2F%28t%2B4%29+=+%28t-7%29%2F%28t%2B5%29+%2B+1
t=1
%281-1%29%2F%281%2B4%29+=+%281-7%29%2F%281%2B5%29+%2B+1
0+=+%28-6%29%2F%286%29+%2B+1
0=0
I leave it to you to verify the t=-3 solution.