Question

divide. if there is a remainder, include it as a simplified fraction.\\((4h^{2}+9h)\div h\\)

Explanation:

Step1: Split the numerator terms

We can split the division of the polynomial by the monomial into two separate divisions: $\frac{4h^2 + 9h}{h}=\frac{4h^2}{h}+\frac{9h}{h}$

Step2: Simplify each term

For the first term, using the rule of exponents $\frac{a^m}{a^n}=a^{m - n}$ (where $a = h$, $m = 2$, $n = 1$), we have $\frac{4h^2}{h}=4h^{2-1}=4h$. For the second term, $\frac{9h}{h}=9$ (since $h/h = 1$). Then we add the two simplified terms together: $4h+9$

Answer:

$4h + 9$