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Im trying to simplify a function whilst already knowing the result that I need to work towards. The function being:

$$\frac{o-n}{3z} = \frac{n}{2z}$$

The result is:

$$n = \frac{2}{5} o$$

I've been trying all kinds of transformations of this in wolfram alpha to see what I'm going wrong but I just can't seem to get there. I'm sure that I'm overlooking something very stupid. Any pointers would be very welcome.

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    the result looks right, if $$z\ne 0$$ – 2017-01-15

1 Answers 1

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We have the equation: $$\frac{o-n}{3z}=\frac{n}{2z}$$ We cross-multiply: $$2z(o-n)=n(3z)$$ Divide both sides by $z$ (Note that this expression only becomes correct when $z\neq 0$): $$2(o-n)=3n$$ Expand: $$2o-2n=3n$$ $$2o=3n+2n$$ $$2o=5n$$ Finally, divide both sides by $5$: $$\boxed{n=\frac{2}{5}o}$$