In mathematics, LHS is informal shorthand for the left-hand side of an equation. Similarly, RHS is the right-hand side. The two sides are in practice interchangeable, since equality is symmetric. This abbreviation is seldom if ever used in print; it is very informal.

More generally, these terms may apply to an inequation or inequality. In the inequality case, there need not be symmetry. The right-hand side is everything on the right side of a test operator in an expression. Conversely, the left-hand side is everything on the left side.

The typical case is of some operatorL, with the difference being that between the equation

Lf = 0,

to be solved for a function f, and the equation

Lf = g,

with g a fixed function, to solve again for f. The point of the terminology appears for L a linear operator. Then any solution of the inhomogeneous equation may have a solution of the homogeneous equation added to it, and still remain a solution.

For example in mathematical physics, the homogeneous equation may correspond to a physical theory formulated in empty space, while the inhomogeneous equation asks for more 'realistic' solutions with some matter, or charged particles.