To solve, first rewrite the equation:
(x^4 + 4x^3 +2x^2 + x + 4) / (x^2 + 3x)
1. Then, you will divide the term with the highest power in the numerator (x^4) by the term in the denominator with the highest power (x^2). When exponents are involved in dividing, you simply subtract them from one another:
x^4 / x^2 = x^2
2. Now, you will multiply this answer by the denominator:
x^2 (x^2 + 3x) = x^4 + 3x^3
3. Next, subtract this answer from the numerator, and bring down the rest:
(x^4 + 4x^3 + 2x^2 + x + 4)
-x^4 - 3x^3
= x^3 + 2x^2 + x + 4
Now, repeat the steps until you're at the simplest form:
1. x^3 / x^2 = x
2. x (x^2 + 3x) = x^3 + 3x^2
3. x^3 + 2x^2 + x + 4
-x^3 - 3x^2
= -x^2 + x + 4
1. -x^2 / x^2 = -1
2. (-1) (x^2 + 3x) = -x^2 - 3x
3. -x^2 + x + 4
+x^2 + 3x
= 4x + 4
