SOLUTION: 4. Two numbers differ by 9 and the sum of their reciprocals is 5/12. Find the numbers.

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Question 1207267: 4. Two numbers differ by 9 and the sum of their reciprocals is 5/12. Find the numbers.
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

1st Hint:
One setup equation would be 1%2Fx+%2B+1%2F%28x%2B9%29+=+5%2F12

2nd hint:
Multiply both sides by the LCD 12x(x+9) to arrive at 12%28x%2B9%29+%2B+%2812x%29+=+5x%28x%2B9%29

3rd hint:
Expand everything out and get terms to one side.
You should get 5x%5E2%2B21x-108=0
In which you can use the quadratic formula.