one interger is 2 more than another. the sum of their reciprocals is 8/15. find both numbers

Question

solve the application. make sure to include a key defining your variables, the equation used for solving and the work solving the equation

Answer 1

1/x + 1/(x + 2) = 8/15

 

The common denominator is 15x(x + 2). Once we find it, we don't need it and we just use the resulting numerators.

 

15(x + 2) + 15x = 8x(x + 2)

15x + 30 + 15x = 8x² + 16x

8x² - 14x - 30 = 0

4x² - 7x - 15 = 0

(4x + 5)(x - 3) = 0

 

4x + 5 = 0

4x = -5 

x = -5/4, not an integer

 

x - 3 = 0

x = 3

 

3 and 5 are your integers.