How do you divide #(x^2+13x+12)/(x+2)div(x+1)#?

To divide (x^2+13x+12)/(x+2) by (x+1), you can use long division or synthetic division. Here is the step-by-step process using long division:

1. Divide the first term of the numerator (x^2) by the first term of the denominator (x). This gives x as the first term of the quotient.
2. Multiply the entire denominator (x+1) by x, and subtract the result from the numerator (x^2+13x+12).
   • (x+1) * x = x^2 + x
   • (x^2+13x+12) - (x^2 + x) = 12x + 12
3. Bring down the next term from the numerator (-12x) and repeat the process.
4. Divide (-12x) by (x) to get -12 as the next term of the quotient.
5. Multiply the entire denominator (x+1) by -12, and subtract the result from the remaining numerator (12x + 12).
   • (x+1) * -12 = -12x - 12
   • (12x + 12) - (-12x - 12) = 24
6. There are no more terms left in the numerator, so the remainder is 24.
7. The final quotient is x - 12 with a remainder of 24.

Therefore, (x^2+13x+12)/(x+2) divided by (x+1) equals x - 12 with a remainder of 24.