Question 958656
x=the number
{{{x+24/x=-11}}} Multiply each side by x.
{{{x^2+24=-11x}}} Add 11x to each side. 
{{{x^2+11x+24=0}}}
{{{(x+3)(x+8)=0}}}
{{{x+3=0}}} or {{{x+8=0}}}
{{{x=-3}}} or {{{x=-8}}} ANSWER The number is -8 or -3.
CHECK:
For (-3):
{{{x+24/x=-11}}}
{{{-3+(24/-3)=-11}}}
{{{-3+(-8)=-11}}}
{{{-11=-11}}}
For (-8):
{{{x+24/x=-11}}}
{{{-8+(24/-8)=-11}}}
{{{-8+(-3)=-11}}}
{{{-11=-11}}}