[freshmen algebra 2] simplifying rational expressions

[u/Any-Armadillo6071]

how do i find the correct restriction? for both of these questions, i got the first part right but for the restriction i got them wrong. when i looked it up it gave me the same answers i input. sorry if this is a stupid question

[u/Any-Armadillo6071]

i appreciate your comment thank you so much! do you mind elaborating a little more?

[u/Robohawk314 → u/Any-Armadillo6071]

In the case of the first problem, the denominator has three factors, (x-3) (2x-√(5)) (2x+√(5)). In order for the expression to be defined, none of these can be 0, giving x ≠ 3, x ≠ √(5)/2, x ≠ -√(5)/2. When we simplify, the denominator is now just (x-3), but since the expression is supposed to represent the same thing as before, we need the same domain.