Solution assignment 05 Inequalities with fractions

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Assignment 5

Solve:

\displaystyle\frac{x}{x-3}>0

Solution

In this fraction both numerator and denominator can take positive or negative numbers. Therefore we draw so-called number lines for both functions and one for the quotient:

x-------------------(0)+++++++++++++
x-3 ----------------------------(3)++++++
result  +++++++++++(0)---------(3)++++++

The quotient is positive if (see the third number line):

x<0 or x>3

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