SOLUTION: I need to find all the values of t. (2/(t-3))+(2/(t-2))=(10/(t^(2)-5t+6))

Algebra ->  Equations -> SOLUTION: I need to find all the values of t. (2/(t-3))+(2/(t-2))=(10/(t^(2)-5t+6))      Log On


   

Question 207651: I need to find all the values of t.
(2/(t-3))+(2/(t-2))=(10/(t^(2)-5t+6))
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2%2F%28t-3%29%2B2%2F%28t-2%29=10%2F%28t%5E2-5t%2B6%29 Start with the given equation.


2%2F%28t-3%29%2B2%2F%28t-2%29=10%2F%28%28t-3%29%28t-2%29%29 Factor the last denominator.


Multiply EVERY fraction by the LCD %28t-3%29%28t-2%29 to clear out the fractions.


%28t-2%292%2B%28t-3%292=10 Simplify


2%28t-2%29%2B2%28t-3%29=10 Rearrange the terms.


2t-4%2B2t-6=10 Distribute.


-10%2B4t=10 Combine like terms on the left side.


4t=10%2B10 Add 10 to both sides.


4t=20 Combine like terms on the right side.


t=%2820%29%2F%284%29 Divide both sides by 4 to isolate t.


t=5 Reduce.


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Answer:

So the solution is t=5