Posted by katy on Friday, September 23, 2011 at 3:55pm.
Think of it as a long division problem, and do it the way you would if dividing a 2-digit number into a 3-digit number.
x goes into x^2 x times.
Multiply the divisor by x to get x^2 + 3x
Subtract that from x^2 + 5x and the x^2 terms go away.
Now you are left with x+3 into 2x+8. x goes into 2x 2 times.
Multiply the divisor by 2 to get 3x+6
Subtract that and the x terms go away, and you are left with a remainder of 2.
So, (x^2 + 5x + 8)/(x + 3) = x+2 remainder 2
or
x + 2 + 2/(x+3)
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