x^2+4x-47

x+8

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To simplify the expression (x^2 + 4x - 47) / (x + 8), we can use polynomial division. Here's how you can do it:

1. Start by dividing the highest degree term of the numerator (x^2) by the highest degree term of the denominator (x). This gives you x.

x
-------
x + 8 | x^2 + 4x - 47

2. Multiply the entire denominator (x + 8) by the result of step 1 (x) and write the product below the numerator.

x
-------
x + 8 | x^2 + 4x - 47
- (x^2 + 8x)

3. Subtract the term obtained in step 2 from the numerator.

x
------------
x + 8 | x^2 + 4x - 47
- (x^2 + 8x)
--------------
-4x - 47

4. Now, bring down the next term from the numerator (-4x) and repeat the process.

x - 4
------------
x + 8 | x^2 + 4x - 47
- (x^2 + 8x)
--------------
-4x - 47
- (-4x - 32)
----------------
-15

5. We have now obtained the remainder, which is -15. The simplified expression is the quotient (x - 4) plus the remainder (-15) over the denominator (x + 8).

Therefore, (x^2 + 4x - 47) / (x + 8) simplifies to (x - 4) - 15 / (x + 8).