math
posted by Sean .
Find the solution where x and y are integers to:
1/x + 1/y = 1/14
I can use a computer to get a list of solutions:
7, 14
10, 35
12, 84
13, 182
15, 210
16, 112
18, 63
21, 42
28, 28
but I'm having trouble solving this analytically and coming to a general formula.

1/x + 1/y = 1/14
(x+y)/xy=1/14 Inverse
xy/(x+y)=14
xy=14x+14y
xy14x=14y
x(y14)=14y
xy=14x+14y
xy14y=14x
y(x14)=14x Divide with (x14)
y=14x/(x14)
Solutions:
x14#0
and
y=14x/(x14) x#0 
Do not forget that, since x and y are symmetric, they are interchangeable on your list.
Example: if (13, 182) works, then (182, 13) works as well. 
Go to:
wolframalpha com
When page be open in rectangle type:
1/x + 1/y = 1/14
and click option =
When you see results couple times click option: More Solutions 
bosnian, i already used wolfram alpha to get the solutions I listed. I want to derive the solution analytically.
anon, I believe you just did algebraic rearrangement.
Respond to this Question
Similar Questions

English
Let's write down what you can do with the computer. 1. I use the computer to chat with netizens in chatrooms. 2. I use the computer to do paper work. 3. I use the computer to make documents with the word processor, Excel. 4. I use … 
math
1. Select any two integers between 12 and +12 which will become solutions to a system of two equations. 2. Write two equations that have your two integers as solutions. Show how you built the equations using your integers. Your solution … 
Alg 1
Diana is driving 182 miles to Orlando for a math convention. She has already driven x miles of th trip. If Diana drives below 70 miles per hour for the remainder of th trip, which inequality best represents the amount of time in hours, … 
Algebra
Solve the following system of equations by the elimination method. 1/3x+1/4y=7 1/3x3/4y=9 a)The solution is___? 
Advanced Math
Planting Depth(in)Height (in) 3 5 6 9 6 18 6 8 7 21 6 12 4 12  a.Write the depths as integers b.list those integers from least to greatest c.write the heights as integers d.list those … 
Chemistry
You have to prepare a pH 3.50 buffer, and you have the following 0.10M solutions available HCOOH, CH3COOH, H3PO4,CHOONa, CH3COONa, and NaH2PO4. a) What solutions would you use? 
UIC
Given a diprotic acid, H2A, with two ionization constants of Ka1 = 3.57× 10–4 and Ka2 = 3.14× 10–12, calculate the pH and molar concentrations of H2A, HA–, and A2– for each of the solutions below. (a) a 0.182 M solution of … 
Math
We can find the solutions of sin x = 0.6 algebraically. (Round your answers to two decimal places.) (a) First we find the solutions in the interval [0, 2π). We get one such solution by taking sin−1 to get x = ________ (smaller … 
algebra
solve for "x": 0.75(8x24)4x=182 6x184x=182 2x=182+18 2x=200 x=100 Check: 0.75(8x24)4x=182 0.75(80024)400=182 0.75 (824)400=182 618400=182? 
physics
Seven measurements of the length of a table in centimeters are 184.7, 182.3, 182.7, 182.1, 182.2, 184.1, and 182.9. Find the best estimate for the length of the table. Be sure to include units! Answer: Seven measurements of the length …