SOLUTION: solve the equation 1/x-2 - 4/x^2-4 = 5 please help me solve this equation

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Question 197269: solve the equation
1/x-2 - 4/x^2-4 = 5
please help me solve this equation
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Ignore the previous post (there is a solution).


1%2F%28x-2%29-4%2F%28x%5E2-4%29+=+5 Start with the given equation.


1%2F%28x-2%29-4%2F%28%28x-2%29%28x%2B2%29%29+=+5 Factor the second denominator


Take note that x%3C%3E-2 or x%3C%3E2 (these values cause a division by zero)





x%2B2-4+=+5%28x-2%29%28x%2B2%29 Simplify


x%2B2-4+=+5%28x%5E2-4%29 FOIL


x%2B2-4+=+5x%5E2-20 Distribute


x-2+=+5x%5E2-20 Combine like terms.


0+=+5x%5E2-20-x%2B2 Get everything to one side.


0+=+5x%5E2-x-18 Combine like terms.


Notice we have a quadratic in the form of Ax%5E2%2BBx%2BC where A=5, B=-1, and C=-18


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%285%29%28-18%29+%29%29%2F%282%285%29%29 Plug in A=5, B=-1, and C=-18


x+=+%281+%2B-+sqrt%28+%28-1%29%5E2-4%285%29%28-18%29+%29%29%2F%282%285%29%29 Negate -1 to get 1.


x+=+%281+%2B-+sqrt%28+1-4%285%29%28-18%29+%29%29%2F%282%285%29%29 Square -1 to get 1.


x+=+%281+%2B-+sqrt%28+1--360+%29%29%2F%282%285%29%29 Multiply 4%285%29%28-18%29 to get -360


x+=+%281+%2B-+sqrt%28+1%2B360+%29%29%2F%282%285%29%29 Rewrite sqrt%281--360%29 as sqrt%281%2B360%29


x+=+%281+%2B-+sqrt%28+361+%29%29%2F%282%285%29%29 Add 1 to 360 to get 361


x+=+%281+%2B-+sqrt%28+361+%29%29%2F%2810%29 Multiply 2 and 5 to get 10.


x+=+%281+%2B-+19%29%2F%2810%29 Take the square root of 361 to get 19.


x+=+%281+%2B+19%29%2F%2810%29 or x+=+%281+-+19%29%2F%2810%29 Break up the expression.


x+=+%2820%29%2F%2810%29 or x+=++%28-18%29%2F%2810%29 Combine like terms.


x+=+2 or x+=+-9%2F5 Simplify.


So the possible solutions are x+=+2 or x+=+-9%2F5

However, recall that we stated that x%3C%3E2 (this values causes a division by zero). So x+=+2 is NOT a solution.


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Answer:


So the only solution is x+=+-9%2F5