Sides of an equation

Example

The expression on the right side of the "=" sign is the right side of the equation and the expression on the left of the "=" is the left side of the equation.

For example, in : x + 5 = y + 8

x + 5 is the left-hand side (LHS) and y + 8 is the right-hand side (RHS).

Homogeneous and inhomogeneous equations

In solving mathematical equations, particularly linear simultaneous equations, differential equations and integral equations, the terminology homogeneous is often used for equations with some linear operator L on the LHS and 0 on the RHS. In contrast, an equation with a non-zero RHS is called inhomogeneous or non-homogeneous, as exemplified by

:Lf = g,

with g a fixed function, which equation is to be solved for f. 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.

Syntax

More abstractly, when using infix notation

:T * U

the term T stands as the left-hand side and U as the right-hand side of the operator *. This usage is less common, though.

References

References

1. [https://books.google.com/books?id=_BhgAwAAQBAJ&dq=rhs+equation&pg=PA65 Engineering Mathematics, John Bird, p65]: definition and example of abbreviation