Distance between moon and earth

[phinl]

Homework Statement

I'm stuck at one of my homework questions.Basically,it says there is a line EM between the Earth's and moon's centre of masses.The moon revolves around the Earth in circular motion.Point X(somewhere in between moon and earth)represents a point where the resultant gravitational force is 0.Mass of moon/Mass of earth=0.012. Given distance EX is 3.4x10^8,determine distance of EM.

Sorry I can't show a diagram.

Homework Equations

F=GMm/r^2

I can only think of this.

The Attempt at a Solution

It's quite lengthy and after some time I realized it was wrong so I think it would be better if I just read some suggested solutions from you guys.

 

[technician]

The point X is at a distance from the centre of the Earth and at a distance from the centre of the Moon.
These 2 distances add up to the separation of the Earth and Moon.
Can you see it... it is an exercise in algebra and substitution of the appropriate distances in your equation.