Question 1190758
<br>
x = smaller integer
x+5 = larger integer<br>
The sum of twice the reciprocal of the lesser integer and thrice the reciprocal of the larger is 5/6:<br>
{{{2/x+3/(x+5)=5/6}}}<br>
Multiply everything by the least common denominator 6(x)(x+5) to clear fractions:<br>
{{{2(6)(x+5)+3(6)(x)=5(x)(x+5)}}}
{{{(12x+60)+18x=5x^2+25x}}}
{{{5x^2-5x-60=0}}}
{{{x^2-x-12=0}}}
{{{(x-4)(x+3)=0}}}<br>
{{{x=4}}} or {{{x=-3}}}<br>
Both solutions satisfy the conditions of the original problem:<br>
{{{2/4+3/9=1/2+1/3=5/6}}}
{{{2/-3+3/2=-2/3+3/2=5/6}}}<br>
ANSWERS: 4 and 9, or -2 and 3<br>