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I am having issues solving the following equation: $\frac{x}{2x-3} - \frac{1}{2x} = \frac{3}{4x-6}$

The resolution of this is 1.

It is in the section of parabolas and it should be pretty easy to solve.

My steps are as follows:

$\frac{x}{2x-3} - \frac{1}{2x} = \frac{3}{4x-6}$ Multiply by $2x(4x-6)$

$4x^2 -1(4x-6) = 6x$ gets me here, remove $6x$

$4x^2 - 10x + 6 = 0$

Solving this with the parabola formula I ended up getting $\{4,6\}$.

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    Done, will have to wait$2$days to be allowed to accept it :)2010-12-08

2 Answers 2

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HINT $\rm\displaystyle\quad \frac{1}{2\ x}\ =\ \frac{2\ x}{4\ x-6} - \frac{3}{4\ x-6}\ =\ \frac{1}2\ \ \Rightarrow\ \ x\ =\ \ldots\quad$ Note: no quadratic formula needed.

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@J. M. :

After checking out the formula I found out that I dividing by $2$ instead of $4a$/$8$

$\frac{10 \pm \sqrt{100-96}}{2}$

With the fixed form I get the results $1.5$ and $1$ of which $1$ is matching result.

Thanks for the kind support!

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    Yup, evil division by $0$ of doom.2010-12-08