Solve the following equation for x. $$\frac{x}{m} - \frac{1}{n} = \frac{3x}{mn}$$

I've tried $$\frac{x}{m} - \frac{1}{n} = \frac{3x}{mn} // \frac{x}{m} x \frac{n}{n} = \frac{3x}{mn} // \frac{xn - m}{mn} = \frac{3x}{mn}$$ This is where I get stuck. I need a tutor!
Your original equation is this and you are asked to isolate $x$;

$$\frac{x}{m} - \frac{1}{n} = \frac{3x}{mn}.$$

If you place the terms on the left hand side over a common denominator you will get this;

$$\frac{nx}{mn} - \frac{m}{mn} = \frac{3x}{mn}.$$

Since the terms on the left hand side have a common denominator, you can rewrite this as follows;

$$\frac{nx - m}{mn} = \frac{3x}{mn}.$$

You now have the left hand side and right hand side over a common denominator and can multiply through by $mn$ to get 

$$nx - m = 3x.$$

Now, this is a lot simpler; collect the $x$ terms, factorise and isolate.

$$nx - m = 3x \implies nx - 3x = m$$

Factorising gives;

$$x(n - 3) = m.$$

Finally, divide through by $(n - 3)$;

$$x = \frac{m}{n -3}.$$

It is important to note that this is only valid for the case where $n \neq 3$ since this would give us an undefined answer.

Happy mathing!
You can easily see that $x= \frac{m}{n-3}$.