Solution assignment 06 Inequalities with fractions

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Assignment 6

Solve:

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

Solution

The numerator and denominator of this fraction can take both positive and negative numbers. For both functions we draw a 'number line' as well as for the quotient:

x-1 -------------------------------(1)++++++
x+2 ------------(-2)++++++++++++++++
result  +++++++++(-2)--------------(1)++++++

The quotient line shows that the fraction is negative if:

-2<x<1

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