Question 103393
{{{1/x+1/(x+1)=7/12}}}
{{{12x*(x+1)*(1/x+1/(x+1))=12x(x+1)*7/12}}} Multiply both sides by 12x*(x+1) to remove all denominators. 
{{{12(x+1)+12x=7x*(x+1)}}}Distributive property and simplify.
{{{12x+12+12x=7x^2+7x}}} Distributive property.
{{{24x+12-24x-12=7x^2+7x-24x-12}}} Additive inverse of 24x+12
{{{7x^2-17x-12=0}}}
Use the quadratic equation,
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
where a=7, b=-17, and c=-12
{{{x = (-(-17) +- sqrt( 17^2-4*7*(-12)))/(2*7) }}}
{{{x = (17 +- sqrt( 289+336))/(14) }}}
{{{x = (17 +- 25)/(14) }}}
{{{x = 42/14 }}} and {{{x=-8/14}}}
Since the answer we are looking for needs to be an integer choose
{{{x=42/14}}} or {{{x=3}}}
Verify your answer. 
{{{1/3 + 1/4 = 7/12}}}
{{{4/12 + 3/12 = 7/12}}}
{{{7/12 = 7/12}}}
Good answer
Two integers are 3 and 4.