Rational Inequality...1

[nycmathguy]

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?

 

[MathLover1]

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)

 

[nycmathguy]

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.

 

[MathLover1]

(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)

 

[nycmathguy]

(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)

I gotta watch video clips to grasp this stiff. Thanks anyway.