The sum of the reciprocals of two numbers is 7. The larger reciprocal exceeds the smaller by 7/3. find the numbers

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The sum of the reciprocals of two numbers is 7. A large reciprocal is 7/3 larger than a small one. Find the number

frac{1}{x}=First number
< img src ="https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bx%7D%2B%5Cfrac%7B7%7D%7B3%7D%3Dsecond%20number" id="TexFormula2 " title ="frac{1}{x}+frac{7}{3}=number of seconds" alt="frac{1}{x}+frac{7}{3}=number of seconds" align="absmiddle" class ="Latex Formula">

frac{1}{x}+frac{1}{x}+frac{7}{3}=7< br / > frac{2}{x}+frac{7}{3}=7
frac{2}{x} =frac{14}{3}
2=frac{14x}{3}
6=14x
x=frac{3}{7}

first number is 3/7, second number is 58/21

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