#(x-1)/(f(x) - f(x+1))#
To solve this, you first have to simplify the denominator. In order to do this, you need to know what #f(x)# is.
They tell us that #f(x+1) = x^2 +x#. This is a start.
#f(x)# seems to equal #x * k#, where #k# means "some number that we don't know yet". To find k, we can rewrite the provided function as this: #x^2 + x = (x + 1)k#.
Now we see that multiplying #(x + 1)# by #x# will give us #x^2 + x#, so #k = x#.
(See that #(x^2 + x)/x = x + 1#.)
Now we can rewrite #f(x)# as #f(n) = nx#.
(I'm using #n# here where I would normally use #x# because it will keep us from getting confused; if I continued to use #x#, my function would say that #f(x) = x^2#, which is not true.)
Now we can plug this into the statement that we need to solve.
#(x-1)/(f(x) - f(x+1)) = (x-1)/((x)(x) - (x+1)(x)#
#(x-1)/(x^2 - (x^2 + x))#
#(x-1)/(x^2 - x^2 - x)#
#x^2 - x^2 = 0#, so we're left with
#(x-1)/-x#
