x^2+8x+15/x^2+x+3
Combine "like" terms. Those would be the two "x" terms only in this case.
x^2+ 8x+ 15/x^2 +x +3
= x^2 +9x +15/x^2 +3
If, however, we're missing parentheses as surmised by Reiny, then we have
(x+5)(x+3)/(x^2 + x + 3)
not much progress there.
What exactly is the objective here? Long division of polynomials?
YES.
To simplify the expression (x^2+8x+15)/(x^2+x+3), we can start by factoring the numerator and the denominator.
The numerator, x^2+8x+15, can be factored into (x+3)(x+5), using the fact that when we multiply the term 3 with the term 5, we get 15, and when we add 3 and 5, we get 8 (which is the coefficient of x).
The denominator, x^2+x+3, cannot be factored further as it does not have any factors that multiply to 3 and add up to 1 (the coefficient of x). Hence, we leave it as is.
Now we substitute the factored forms back into the expression:
[(x+3)(x+5)] / (x^2+x+3)
Next, we observe that there are no common factors between the numerator and the denominator. Thus, we cannot cancel out any terms.
So, the simplified form of the expression (x^2+8x+15)/(x^2+x+3) is [(x+3)(x+5)] / (x^2+x+3).
Note: Another way to simplify the expression is by applying division or long division algorithm, but it may be a bit more cumbersome.