An expression can easily be simplified by combining like terms and performing basic arithmetic operations on it. Parentheses ( ) and brackets [ ] can be used to group terms, and while simplifying an expression it is good to follow the order of operations.

For example, $\frac{x^{2}-1}{x+1}$ can be written as $\frac{x^{2}-1}{x+1}$ = $\frac{(x+1)(x-1)}{x+1}$. Strike out the common factor (x + 1) as it is the common term. Therefore the solution is (x - 1).

Algebraic expressions contains variables and also numbers. When an algebraic expression is simplified the resulting expression will be simpler than the original. There is no standard procedure for simplifying algebraic expressions as they are of different kinds.
However they can grouped into three types:

1. Easy to simplify.
2. Need some preparation while simplifying.
3. Cannot be simplified.

Solved Example

Question: Simplify : 7x + 8y + 2 + 4x - 7y + 5
Solution:
 
The given expression can be easily simplified by grouping and combining like terms.
7x + 4x  when combined gives 11x,
8y - 7y  is y and,
2 + 5 is 7.
Therefore the resulting expression is 11x + y + 7.