show the function is uniformly ctns on the (2,8)

Question

[show the function f(x)=(2x^5-98)/(x-9)(x-1) is uniformly continuous on the interval(2,8)

I found it need to show the function is uniformly ctns in [2,8] then I can say (2,8)>=[2,8]

I am still confused how to show the function ctns in [2,8]. It is hard to use direct way to prove that.]2

Answer 1

Every rational function is continuous on its domain. (The sum, difference, product, quotient of continuos unctions is continuous - just keep in mind that the quotient may have a smaller domain)