\(x=\frac{21}{31} \)
LCM or Least Common Multiplier of 3&7 = 21
\(\frac{x}{7}\cdot \:21+\frac{x}{3}\cdot \:21=1\cdot \:21-x\cdot \:21\)
Simplify:
\(3x+7x=21-21x \)
\(10x=21-21x\)
Add 21x to both sides:
\(10x+21x=21-21x+21x \)
\(31x=21\)
Divide:
\(\frac{31x}{31}=\frac{21}{31}\)
\(x=\frac{21}{31}\)
Hope it helps! :)