Question

find the domain of each rational expression each polunomial must be fully factored and that you can only cancel factors you can not cancel terms. x^2-49 over 2x-1 and x^2-14+49 over 1-2x

Answer 1

first one:

(x-7)(x+7)/(2x-1)

well all x are ok, except for x=1/2: division by zero is not defined.

range:
consider look at the transition of sign changes: at x=-7, x=7, and x=1/2

at x=-8, signs are -*-/- or negative
at x=-6, signs are -*+/- or positive
at x= .55, signs are -*+/+ or negative
at x=8, signs are +*+/+ or positive

so the range is from -inf to +inf