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If 1/x + 1/y = 1/3 and 1/x - 1/y = 1/7, what is the value of x + y? Express your answer as a common fraction.

 May 12, 2022
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\(\) What is the value of x + y?

 

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\(\frac{1}{x}=a;\ \frac{1}{y}=b\\ a+b=\frac{1}{3}\\ \underline{a-b=\frac{1}{7}}\\ 2a=\frac{1}{3}+\frac{1}{7}\\ 42a=10\\ a=\frac{5}{21}\\ \color{blue}x=\frac{21}{5}\)

\(b=\frac{1}{3}-\frac{5}{21}\\ 21b=2\\ b=\frac{2}{21}\\ \color{blue}y=\frac{21}{2}\\ x+y=\frac{21}{5}+\frac{21}{2}=\frac{42+105}{10}\\ \color{blue}x+y=\frac{147}{10}\)

 May 12, 2022

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