SOLUTION: I need help with this homework problem: t+22/t square-t-72 + 8/t-9 = 4/t+8 Thank you.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I need help with this homework problem: t+22/t square-t-72 + 8/t-9 = 4/t+8 Thank you.      Log On


   

Question 144708: I need help with this homework problem:
t+22/t square-t-72 + 8/t-9 = 4/t+8
Thank you.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28t%2B22%29%2F%28t%5E2-t-72%29%2B%288%29%2F%28t-9%29=%284%29%2F%28t%2B8%29 Start with the given equation


%28t%2B22%29%2F%28%28t-9%29%28t%2B8%29%29%2B%288%29%2F%28t-9%29=%284%29%2F%28t%2B8%29 Factor t%5E2-t-72 to get %28t-9%29%28t%2B8%29



Multiply every term by the LCD %28t-9%29%28t%2B8%29 to clear out the fractions



Cancel like terms


%28t%2B22%29%2B%28t%2B8%298=%28t-9%294 Simplify


t%2B22%2B8t%2B64=4t-36 Distribute



9t%2B86=4t-36 Combine like terms on the left side


9t=4t-36-86Subtract 86 from both sides


9t-4t=-36-86 Subtract 4t from both sides


5t=-36-86 Combine like terms on the left side


5t=-122 Combine like terms on the right side


t=%28-122%29%2F%285%29 Divide both sides by 5 to isolate t



t=-122%2F5 Reduce

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Answer:
So our answer is t=-122%2F5 (which is approximately t=-24.4 in decimal form)