(x^2 - 8x + 6)/(x + 2)

= x - 10 + ((26)/(x + 2))

To simplify the expression (x^2 - 8x + 6)/(x + 2), you can use polynomial long division or synthetic division. In this case, we will use polynomial long division.

Step 1: Divide the first term of the numerator (x^2) by the first term of the denominator (x). The result is x.

x
----------
x + 2 | x^2 - 8x + 6

Step 2: Multiply the divisor (x + 2) by the result of the division (x), and subtract the product from the numerator.

x
----------
x + 2 | x^2 - 8x + 6
- (x^2 + 2x)
-----------
-10x + 6

Step 3: Bring down the next term from the numerator (-10x). We now have -10x + 6.

x - 10
----------
x + 2 | x^2 - 8x + 6
- (x^2 + 2x)
-----------
-10x + 6

Step 4: Divide the first term of the new numerator (-10x) by the first term of the denominator (x). The result is -10.

x - 10
----------
x + 2 | x^2 - 8x + 6
- (x^2 + 2x)
-----------
-10x + 6
- (-10x - 20)
----------------
26

Step 5: Multiply the divisor (x + 2) by the result of the division (-10), and subtract the product from the previous result (-10x + 6).

x - 10 + (26/(x + 2))
-----------------------------
x + 2 | x^2 - 8x + 6
- (x^2 + 2x)
-----------
-10x + 6
- (-10x - 20)
----------------
26

Therefore, the simplified expression is x - 10 + (26/(x + 2)).