What is a quote in the book that shows how Jay Gatsby views life?
Most of the choice quotes about how to view life belong to Nick. As the narrator and the outsider to this world as we are, the best lines about life belong to Nick. Adding to this challenge is that Gatsby really lacks the reflective element that affords him a profound world view. If he had this element, he would have not been involved with Daisy and would have understood the entire "fairy's wing" thing a bit more. In any event, I do believe that we can pull some quotes from Gatsby that do talk about how he conceives of being in the world. Consider one such example about how Gatsby "makes his money:"
"Oh, I've been in several things," he corrected himself. "I was in the drug business and then I was in the oil business. But I'm not in either one now."
The ability to "remake" oneself, to define one's own being through their own "Platonic conception of self," is what drives Gatsby. It represents a view he has on life: There is nothing that cannot be appropriated through the lens of the mind's eye.
It is in this where one sees how Gatsby views life. Gatsby is able to see that his own being is something that he can construct and conceive in his own thoughts and actions. He can do "several things" and not be limited by any of them. He leaves and enters new professions in accordance to his ability to remake and redefine himself in accordance to his own understanding of self. For Gatsby, life is the ability to use freedom to get what one wants and this construction of self is the only element that matters. One sees that in how he describes what he does to Nick.
Gatsby says to Nick, "Can't repeat the past? Why, of course you can!"
And that in itself sums up Gatsby's whole life view. Gatsby is dedicated to pursuing the his past glories of love and romance; failing to realize that whatever he "achieves" is just a paltry illusion of the past. This obsession with the past is both his life view and fatal flaw.