My Math Forum Solving Equation/Inequality

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December 16th, 2012, 04:21 PM   #1
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Solving Equation/Inequality

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 December 16th, 2012, 06:43 PM #2 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,963 Thanks: 1148 Math Focus: Elementary mathematics and beyond Re: Solving Equation/Inequality $\fbox{1}$ $\frac{7x}{x\,-\,7}\,-\,\frac{4}{x}\,=\,\frac{28}{x^2\,-\,7x}$, x ? 0, x ? 7. $\frac{7x^2\,-\,4(x\,-\,7)}{x^2\,-\,7x}\,=\,\frac{28}{x^2\,-\,7x}$ $7x^2\,-\,4(x\,-\,7)\,=\,28$ $7x^2\,-\,4x\,+\,28\,=\,28$ $7x^2\,-\,4x\,=\,0$ $7x^2\,=\,4x$ $7x\,=\,4$ $x\,=\,\frac47$ $\fbox{2}$ $\frac{2x\,+\,2}{2x^2\,+\,5}\,>\,0$ The denominator is always positive (do you see why?) so we are only concerned with where the numerator is positive, i.e. greater than zero: $2x\,+\,2\,>\,0\,\Rightarrow\,x\,\in\,(-1,\,\infty)$

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