SOLUTION: Please Help me solve this equation: 3t-5 2t ----- =2+ ------ t-1 1-t

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Question 251721: Please Help me solve this equation: 3t-5 2t
----- =2+ ------
t-1 1-t
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%283t-5%29%2F%28t-1%29=2%2B%282t%29%2F%281-t%29 Start with the given equation.


%283t-5%29%2F%28t-1%29=2%2B%282t%29%2F%28-1%28-1%2Bt%29%29 Factor out a -1 from 1-t to get -1%28-1%2Bt%29


%283t-5%29%2F%28t-1%29=2%2B%282t%29%2F%28-1%28t-1%29%29 Rearrange the terms.


%283t-5%29%2F%28t-1%29=2-%282t%29%2F%28t-1%29 Reduce.


Multiply EVERY term by the LCD t-1 to clear out the fractions.


3t-5=2%28t-1%29-2t Simplify.


3t-5=2t-2-2t Distribute.


3t-5=-2 Combine like terms on the right side.


3t=-2%2B5 Add 5 to both sides.


3t=3 Combine like terms on the right side.


t=%283%29%2F%283%29 Divide both sides by 3 to isolate t.


t=1 Reduce.


So the possible solution is t=1, but we need to check it.


Check:


%283t-5%29%2F%28t-1%29=2%2B%282t%29%2F%281-t%29 Start with the given equation.


%283%281%29-5%29%2F%281-1%29=2%2B%282%281%29%29%2F%281-1%29 Plug in t=1


%283-5%29%2F%281-1%29=2%2B%282%29%2F%281-1%29 Multiply


-2%2F0=2%2B2%2F0 Subtract


Since you CANNOT divide by zero, this means that t=1 is NOT in the domain. So t=1 can't be a solution.


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Answer:


So there are no solutions to the equation %283t-5%29%2F%28t-1%29=2%2B%282t%29%2F%281-t%29