How to break long expressions into multiple lines?

Question

Say I want to write a long radical expression like this

$\sqrt{a + b - c + d - e + f - g + h - i + j…}$

on paper or blackboard. It cannot fit in one line. How should I break it into two lines?

Another troubling kind of long expression is fraction. How should I break something like this

$\frac{a + b - c + d - e + f - g + h - i + j…}{A + B - C + D - E + F - G + H - I + J…}$

if numerator or denominator cannot fit in one line?

Answer 1

This is a typographic question rather than a mathematical one.

There really is no good way. That said, when you find yourself in a situation where you want to write such things, please think about your audience. Whether or not you find a "good" way to write it, your reader will have a hard time taking it in. There are too many items to keep track of.

If possible, organize the exposition so that you can discuss meaningful parts of the formula separately, and name them. For example

Let $$X = a + b + c,$$ $$Y = d + e + f$$ and $$Z = g + h + i$$ and consider

$$ W = \sqrt{ X - Y + Z} .$$