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Here is the question:

$$ \frac 23 \div x = \frac 12 + \frac 13 .$$

I would be very grateful if someone could find the value of $x$.

Thank You.

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3  
$${{2/3}\over x}={1\over 2}+{1\over3}\iff {{2/3}\over x}={5\over 6} \iff {x\over {2/3}}={6\over 5} \iff x={6\over5}\cdot{2\over3}={4\over 5}$$ – David Mitra Dec 4 '11 at 21:44
up vote 3 down vote accepted

Note that $$\frac{1}{2} + \frac{1}{3} = \frac{3+2}{6} = \frac{5}{6}.$$ So what you have is equivalent to $$\frac{2}{3}\div x = \frac{5}{6}.$$ Note that $x$ cannot be zero. Multiplying both sides by $x$, we get $$\frac{2}{3} = \frac{5}{6}x.$$ Can you solve it now?

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Yes Thank you very much! The answer is 4/5! – Thomas Ruland Dec 4 '11 at 21:53

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