Editing Sides of an equation

{{Short description|Mathematical nomenclature}}
{{Refimprove|date=December 2009}}
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 (mathematics)|equality]] is [[equivalence relation|symmetric]].<ref>[https://books.google.com/books?id=_BhgAwAAQBAJ&dq=rhs+equation&pg=PA65 Engineering Mathematics, John Bird, p65]: definition and example of abbreviation</ref>

More generally, these terms may apply to an [[inequation]] or [[inequality (mathematics)|inequality]]; the right-hand side is everything on the right side of a [[test operator]] in an [[Expression (mathematics)|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
:<math> x + 5 = y + 8 </math>

{{math|''x'' + 5}} is the '''left-hand side''' (LHS) and {{math|''y'' + 8}} is the '''right-hand side''' (RHS).

==Homogeneous and inhomogeneous equations==
In solving mathematical equations, particularly [[linear simultaneous equations]], [[differential equation]]s and [[integral equation]]s, 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 [[Free space|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 [[Operation (mathematics)|operator]] *. This usage is less common, though.

==See also==
* [[Equals sign]]

==References==
<References/>

{{DEFAULTSORT:Sides Of An Equation}}
[[Category:Mathematical terminology]]