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September 2nd, 2019, 04:58 AM  #1 
Newbie Joined: Sep 2019 From: Greece Posts: 3 Thanks: 0  How to solve an algebraic equation with fractions with an unknown in the denominator
There must be something simple I'm missing here, but this just isn't working out for me. How do I solve: (3 / 5x)  (2 / 6x) = (2 / x) + (7 / 3x) I will probably kick myself when I see the solution... Thanks in advance! 
September 2nd, 2019, 07:18 AM  #2  
Math Team Joined: Jul 2011 From: Texas Posts: 3,101 Thanks: 1677  Quote:
multiply every term by x ... $\dfrac{3}{5}  \dfrac{2}{6} = 2 + \dfrac{7}{3}$ $\dfrac{4}{15} = \dfrac{13}{3}$ ... a contradiction. So, what can you say about the solution?  
September 2nd, 2019, 07:24 AM  #3 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,700 Thanks: 2682 Math Focus: Mainly analysis and algebra 
I think there's an error in what you have written, but in general you would multiply by denominators to get all the $x$s in the numerators. e.g. \begin{align}&& \frac{3}{5x}\frac{2}{5} &= \frac{2}{x} + \frac{7}{5} \\ &\text{(multiply by $5x$)}& 3  2x &= 10 + 7x \\ && 7 &= 9x \\ && x &= \frac79\end{align} In your case, multiplying by $x$ will make all of them go away which is why I think you have made a mistake. 
September 2nd, 2019, 01:05 PM  #4 
Newbie Joined: Sep 2019 From: Greece Posts: 3 Thanks: 0  
September 2nd, 2019, 01:10 PM  #5  
Newbie Joined: Sep 2019 From: Greece Posts: 3 Thanks: 0  Quote:
 

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algebraic, denominator, equation, equations, fractions, solve, solving, unknown 
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