the difference between a positive fraction and its reciprocal is 9/20 find the sum of that fraction and its reciprocal.

• x = the number
  1/x is the reciprocal of the number
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  x - (1/x) = 9/20
  multiply both sides by x to get:
  x^2 - 1 = (9/20)*x
  subtract (9/20)*x from each side of the equation to get:
  x^2 - (9/20)*x - 1 = 0
  multiply both sides of the equation by 20 to get:
  20x^2 - 9x - 20 = 0
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  using the quadratic formula of -b+-_/b^2-4ac / 2a gets me:
  x = 50/40
  or:
  x = -32/40
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  x = -32/40 is rejected because it is not positive and the problem stated that it had to be a positive fraction.
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  your answer is x = 50/40 which is the same as:
  x = 5/4
  
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  to confirm this answer is correct, substitute in the original equations.
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  if we let x = 5/4, then:
  x - (1/x) = 9/20 becomes:
  
  5/4 - 1/5/4 = 9/20
  5/4 - 4/5 = 9/20
  
  this is the same as:
  %285%2F4%29+-+%284%2F5%29+=+9%2F20
  this becomes:
  25-16/20 = 9/20
  which becomes:
  9/20 = 9/20 confirming that x = 5/4 is good.
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  your question was:
  find the sum of the fraction and it's reciprocal.
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  the answer is:
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  if x = 5/4, then 1/x = 4/5 and the sum is 5/4 + 4/5 = (25+16)/20 = 41/20
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