Sides of an equation
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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. 
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). Suppose x=2 then 2+5=7 And y=2 then 2+8=10
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, 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. 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.
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.
- Engineering Mathematics, John Bird, p65: definition and example of abbreviation