# Sides of an equation

In mathematics, **LHS** is informal shorthand for the **left-hand side** of an equation. Similarly, **RHS** is the **right-hand side**. The two sides have the same value, expressed differently, since equality is symmetric.[1]

More generally, these terms may apply to an inequation or inequality; the right-hand side is everything on the right side of a test operator in an expression, with LHS defined similarly.

## 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.

## See also

## References

- Engineering Mathematics, John Bird, p65: definition and example of abbreviation