Simplifying the Expression (m^2  7m  11)/(m  8)
This expression represents a rational function, a fraction where the numerator and denominator are polynomials. Simplifying it involves dividing the numerator by the denominator. There are two primary approaches:
1. Polynomial Long Division
Steps:

Set up the division:
_______ m  8  m^2  7m  11

Divide the leading terms:
 m into m^2 goes m times.
 Write 'm' above the line.
m _______ m  8  m^2  7m  11 m^2  8m 

Subtract:
 Subtract the entire line below.
m _______ m  8  m^2  7m  11 m^2  8m  m  11

Bring down the next term:
 Bring down '11'.

Repeat the process:
 m into m goes 1 time.
 Write '+1' above the line.
m + 1 _______ m  8  m^2  7m  11 m^2  8m  m  11 m  8  3

The result:
 The simplified form is: m + 1  3/(m  8)
2. Factoring
While the numerator does not factor easily, this method could be used if it did.
Steps:

Factor the numerator (if possible):
 In this case, the numerator does not factor easily using standard techniques.

Cancel common factors:
 If there were any common factors, they would be cancelled from both numerator and denominator.
Conclusion
The simplified form of the expression (m^2  7m  11)/(m  8) is m + 1  3/(m  8). This is obtained through polynomial long division. Factoring is not applicable in this specific case due to the numerator's lack of easily identifiable factors.