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Solution assignment 04 Equations with fractions

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Assignment 4

Solve:

\displaystyle\frac{1}{x}=\displaystyle\frac{x+2}{x+3}

Solution

Cross-multiplication yields:

x(x+2)=x+3

x^2+2x=x+3

x^2+x-3=0

This equation can be solved by applying the abc-formula, see also Quadratic equations (abc-formula):

x_{1,2}=\displaystyle\frac{-1\pm\sqrt{13}}{2}

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