What is the limit of #((5u^4)+8)/((u^2)-5)((7u^2)-1)# as x goes to infinity?
It is not clear what the intended question is.
I shall assume that the variables should not be
(if they should be different, there is not enough information to determine the limit.)
# = lim_(xrarroo)(35u^6-5u^4+56u^2-8)/(u^2-5) = oo#
(The degree of the numerator is greater than the degree of the denominator, so the limit is either
If the intended limit is
Then we have:
# = (x^4(5+8/x^4))/(x^4(7-36/x^2+5/x^4)) = 5/7#