Section 2.7 Question 42 (x^2 - 1)/x < 0 Replace < with the equal sign. x • (x^2 - 1)/x = 0 • x x^2 - 1 = 0 (x - 1)(x + 1) = 0 Setting each factor to zero, the key numbers are clearly x = -1 and x = 1. Plot on the real number line and test the original rational inequality per interval. <----------(-1)---------------(1)---------------> When x = -2, we get-3/2 < 0. True statement. When x = -1, we get 0 < 0. False statement. When x = 0, we get -1/0 which is undefined. When x = 1, we get 0/1 < 0. False statement. When x = 2, we get 3/2 < 0. False statement. The only interval that satisfies the original inequality is (-infinity, -1). Here is the solution set on the real number line: You say?
that is one solution and it's correct ( x<-1) other solution is 0<x<1 so interval notation for both solutions: ( infinity, -1), (0, 1)
Can you break it step by step? How did you get two solution sets? In fact, I will watch a few rational inequality clips on You Tube.
(x^2 - 1)/x < 0 if (x^2 - 1)< 0 => solutions: x<1 or x<-1 denominator cannot be equal to zero, we exclude zero and solution is 0<x<1 combine x<-1 and 0<x<1 interval: ( infinity, -1), (0, 1)
