SOLUTION: solve 6/(x^2-9)- 1/(x-3) = 1 the 6 is the numerator and (x^2-9) is the denominator for the first part of the problem and 1 is the numerator for the second fraction and (x

Algebra ->  Algebra  -> Rational-functions -> SOLUTION: solve 6/(x^2-9)- 1/(x-3) = 1 the 6 is the numerator and (x^2-9) is the denominator for the first part of the problem and 1 is the numerator for the second fraction and (x      Log On

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Question 191958: solve

6/(x^2-9)- 1/(x-3) = 1

the 6 is the numerator and (x^2-9) is the denominator for the first part of the problem and 1 is the numerator for the second fraction and (x-3) is the denominator and 1 is the answer? im not sure, im just suppose to solve it


thank you
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
6%2F%28x%5E2-9%29-+1%2F%28x-3%29+=+1 Start with the given equation.


6%2F%28%28x%2B3%29%28x-3%29%29-+1%2F%28x-3%29+=+1 Factor the first denominator


cross%28%28x%2B3%29%28x-3%29%29%286%2F%28cross%28%28x%2B3%29%28x-3%29%29%29%29-+%28x%2B3%29cross%28%28x-3%29%29%281%2Fcross%28%28x-3%29%29%29+=+1%28x%2B3%29%28x-3%29 Multiply EVERY term by the LCD %28x%2B3%29%28x-3%29


6-%28x%2B3%29=%28x%2B3%29%28x-3%29 Multiply and simplify


6-x-3=%28x%2B3%29%28x-3%29 Distribute


-x%2B3=%28x%2B3%29%28x-3%29 Combine like terms.


-x%2B3=x%5E2-9 FOIL


0=x%5E2-9%2Bx-3 Get everything to the right side


0=x%5E2%2Bx-12 Combine like terms.


0=%28x%2B4%29%28x-3%29 Factor


x%2B4=0 or x-3=0 Set each factor equal to zero


x=-4 or x=3 Solve for "x" in each case



So the possible solutions are x=-4 or x=3


However, if you plug in x=3, you'll see that a division by zero occurs. So x=3 is NOT a solution (it's not even in the domain)



So the only solution is x=-4