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 October 31st, 2010, 09:57 AM #1 Member   Joined: Jan 2010 Posts: 32 Thanks: 0 Tricky Algebra Problem Havig hard time solving this tricky algebra problem. Any help is much appreciated.... If n is a natural number, solve the below equation for n: (5/n + n/17)/(3/11 - n/89) = 224191/27540
 October 31st, 2010, 11:00 AM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,193 Thanks: 504 Math Focus: Calculus/ODEs Re: Tricky Algebra Problem $\dfrac{\dfrac{5}{n}+\dfrac{n}{17}}{\dfrac{3}{11}-\dfrac{n}{89}}=\dfrac{224191}{27540}$ Multiply LHS by $\dfrac{11\cdot 17\cdot 89\cdot n}{11\cdot 17\cdot 89\cdot n}$ and factor RHS $\dfrac{5\cdot 11\cdot 17\cdot 89+11\cdot\89\cdot n^2}{3\cdot 17\cdot 89\cdot n-11\cdot 17\cdot n^2}=\dfrac{11\cdot 89\cdot 229}{2^2\cdot 3^4\cdot 5\cdot 17}$ Multiply through by $\dfrac{17}{11\cdot 89}$ $\dfrac{5\cdot 17+ n^2}{3\cdot 89\cdot n-11\cdot n^2}=\dfrac{229}{2^2\cdot 3^4\cdot 5}$ Cross multiply. $137700+1620n^2=61143n-2519n^2$ Add $2519n^2-61143n$ to both sides. $4139n^2-61143n+137700=0$ Factor. $(4139n-11475)(n-12)=0$ The root $n=\dfrac{11475}{4139}$ is not a natural number, but the root $n= 12$ is.
 October 31st, 2010, 02:01 PM #3 Member   Joined: Jan 2010 Posts: 32 Thanks: 0 Re: Trcicky Algebra Problem Thank you so much for your help!

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