Question 294753
Consecutive odd integers follow the pattern: x, x+2, ...



So adding their reciprocals to get {{{12/35}}} means that {{{1/x+1/(x+2)=12/35}}}



{{{1/x+1/(x+2)=12/35}}} Start with the given equation



{{{35(x+2)+35x=12x(x+2)}}} Multiply EVERY term by the LCD {{{35x(x+2)}}} to clear out the fractions.



{{{35x+70+35x=12x^2+24x}}} Distribute




{{{70x+70=12x^2+24x}}} Combine like terms.



{{{0=12x^2+24x-70x-70}}} Get every term to one side.



{{{0=12x^2-46x-70}}} Combine like terms.



*[invoke quadratic_formula 12, -46, -70, "x"]



Since we're only looking for integer values of 'x', we can ignore {{{x=-7/6}}}.



So the only answer is {{{x=5}}} which means that the two consecutive odd integers are 5 and 7.



Notice how {{{1/5+1/7=7/35+5/35=(7+5)/35=12/35}}} which confirms our answer.