we have
g(x)= x+1
f(x)= x² - 10x -11
we know that
(f/g)(x)=f(x)/g(x)
so
substitute
(f/g)(x)=(x² - 10x -11)/(x+1)
simplify the numerator
we have
(x² - 10x -11)=(x+1)(x-11) -------> by complete the square
substitute in the expression above
(f/g)(x)=(x+1)(x-11)/(x+1)
simplify but remember that the value of x can not be equal to -1 (denominator can not be a zero)
we have
(f/g)(x)=x-11
the exceptions is x=-1