The difference between the reciprocals of two consecutive positive odd integers 2/15 . find the intergers

3 and 5

Step-by-step explanation:

consecutive odd numbers have a difference of 2 between them.

let the consecutive odd numbers be n and n + 2, then

the reciprocals are and

The difference between the reciprocals is then

- =

combine the fractions into a single fraction

=

= ( cross- multiply )

2n(n + 2) = 30 ( divide both sides by 2 )

n(n + 2) = 15

n² + 2n - 15 = 0 ← in standard form

(n + 5)(n - 3) = 0 ← in factored form

equate each factor to zero and solve for n

n + 5 = 0 ⇒ n = - 5

n - 3 = 0 ⇒ n = 3

but n > 0 ⇒ n = 3

The 2 integers are n = 3 and n + 2 = 3 + 2 = 5

the correct option is b

step-by-step explanation: