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Question 132604: Two numbers differ by 6 and their reciprocals differ by 8/15.Find the numbers
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! First number: 
Second number: 
The two numbers differ by 6:  We'll just assume that 
The reciprocal of the first number:  ,  and because of , 
The reciprocal of the second number:  ,  and because of , 
Their reciprocals differ by 8/15: Since we have assumed that ,  , so 
Re-write the first equation to solve it for x:
Substitute this expression for x into the second equation in place of x.
Multiply both sides by 15:
Lowest common denominator is just the product of the two denominators since there are no common factors. So:
Distribute and collect like terms all on the left:
Solve the numerator expression for 0, remembering to exclude 0 and -6 as values not in the domain of the function in terms of y.
Divide by -2:
Factor:
 , so y = 1.5 or y = -7.5
y = 1.5 => x = 7.5 because  , so:
 and the first root checks.
y = -7.5 => x = -1.5 because  , so:
 and the second root checks.
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