what should be added to twice the rational number
![- \frac{ 7}{3} \: to \: get \: \frac{3}{7} - \frac{ 7}{3} \: to \: get \: \frac{3}{7}](https://tex.z-dn.net/?f=+-++%5Cfrac%7B+7%7D%7B3%7D+%5C%3A++to+%5C%3A+get+%5C%3A++%5Cfrac%7B3%7D%7B7%7D+)
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twice of rational number
![- \frac{ 7}{3} = - \frac{7}{3} \times 2 \\ = \frac{ - 14}{3} - \frac{ 7}{3} = - \frac{7}{3} \times 2 \\ = \frac{ - 14}{3}](https://tex.z-dn.net/?f=+-++%5Cfrac%7B++7%7D%7B3%7D++%3D++-++%5Cfrac%7B7%7D%7B3%7D++%5Ctimes+2+%5C%5C++%3D++%5Cfrac%7B+-+14%7D%7B3%7D+)
now let the number added be x
so we have
![- \frac{14}{3} + x = \frac{3}{7} \\ x = \frac{3}{7} + \frac{14}{3} \\ x = \frac{9}{21} + \frac{98}{21} \\ = \frac{107}{21} - \frac{14}{3} + x = \frac{3}{7} \\ x = \frac{3}{7} + \frac{14}{3} \\ x = \frac{9}{21} + \frac{98}{21} \\ = \frac{107}{21}](https://tex.z-dn.net/?f=+-++%5Cfrac%7B14%7D%7B3%7D++%2B+x+%3D++%5Cfrac%7B3%7D%7B7%7D++%5C%5C+x+%3D++%5Cfrac%7B3%7D%7B7%7D++%2B++%5Cfrac%7B14%7D%7B3%7D++%5C%5C+x+%3D++%5Cfrac%7B9%7D%7B21%7D++%2B++%5Cfrac%7B98%7D%7B21%7D++%5C%5C++%3D++%5Cfrac%7B107%7D%7B21%7D+)
so
![\frac{107}{21} should \: be \: added \\ hope \: it \: helps \: dear \: \frac{107}{21} should \: be \: added \\ hope \: it \: helps \: dear \:](https://tex.z-dn.net/?f=+%5Cfrac%7B107%7D%7B21%7D+should+%5C%3A+be+%5C%3A+added+%5C%5C+hope+%5C%3A+it+%5C%3A+helps+%5C%3A+dear+%5C%3A+)
☺️✌️
now let the number added be x
so we have
so
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