D What is the Missing Step in this Electrostatic Algebra Equation?

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SUMMARY

The discussion centers on an electrostatic algebra equation related to seesaws, specifically the manipulation of fractions in the equation. The participant initially struggles with understanding how terms cancel out in the equation, particularly in the transition from the first to the second line. The conclusion reached is that there is no missing step; rather, the fractions can be combined directly due to their common denominator, leading to the simplified form. The correct interpretation is that (2q Q)/(4πε_o r²) + (q Q)/(4πε_o r²) simplifies to (3q Q)/(4πε_o r²).

PREREQUISITES
  • Understanding of electrostatic forces and equations
  • Familiarity with algebraic manipulation of fractions
  • Knowledge of the constants involved, such as ε_o (permittivity of free space)
  • Basic principles of equilibrium in physics
NEXT STEPS
  • Review the concept of electrostatic forces and their applications in physics
  • Practice algebraic manipulation of fractions in physics equations
  • Study the derivation and significance of ε_o in electrostatics
  • Explore examples of equilibrium in electrostatic systems
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Students studying physics, particularly those focusing on electrostatics, as well as educators looking for examples of algebraic applications in physical equations.

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Homework Statement



I have a homework question on electrostatic seesaws. My problem is the algebra.

Homework Equations



I have been following another example and any guidance to help me proceed would be great.

0= (2q Q)/(4πε_o r²)+(q Q)/(4πε_o r²)-m
0= (3q Q)/(4πε_o r²)-m
m=(3q Q)/(4πε_o r²)

I don't understand line 2. I don't understand how part of the equation has canceled out. I know there is a step missing so could anyone point me in the right direction.

The Attempt at a Solution

 
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There is no step missing.

There are two fractions which are the same, therefore they can be added:
\frac{2x}{y} + \frac{x}{y} = \frac{3x}{y}
 
Of course! Thank you compuchip x
 

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