Solution assignment 09 Inequalities with fractions

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Assignment 9

Solve:

\displaystyle\frac{x}{x^2-1}<0

Solution

We can factorize the denominator:

\displaystyle\frac{x}{(x+1)(x-1)}<0

We draw a number for each factor.

x-------------------------------(0)+++++++++++
x-1 ------------------------------------(1)++++
x+1 -----------(-1)++++++++++++++++
result -------------(-1)++++(0)--------(1)++++

The solution is:

x<-1 or 0<x<1

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