Answer :
To solve the division
[tex]$$\frac{36x^4 + 12x^8}{12x^4},$$[/tex]
we can split the expression into two fractions:
[tex]$$
\frac{36x^4}{12x^4} + \frac{12x^8}{12x^4}.
$$[/tex]
Step 1: Divide the first term
Divide the coefficients and subtract the exponents of like bases:
[tex]$$
\frac{36x^4}{12x^4} = \frac{36}{12} \cdot \frac{x^4}{x^4} = 3 \cdot 1 = 3.
$$[/tex]
Step 2: Divide the second term
Again, divide the coefficients and subtract the exponents (using the property [tex]$x^a/x^b = x^{a-b}$[/tex]):
[tex]$$
\frac{12x^8}{12x^4} = \frac{12}{12} \cdot \frac{x^8}{x^4} = 1 \cdot x^{8-4} = x^4.
$$[/tex]
Step 3: Combine the results
Now, add the two parts together:
[tex]$$
3 + x^4.
$$[/tex]
Thus, the result of the division is
[tex]$$\boxed{3 + x^4}.$$[/tex]
[tex]$$\frac{36x^4 + 12x^8}{12x^4},$$[/tex]
we can split the expression into two fractions:
[tex]$$
\frac{36x^4}{12x^4} + \frac{12x^8}{12x^4}.
$$[/tex]
Step 1: Divide the first term
Divide the coefficients and subtract the exponents of like bases:
[tex]$$
\frac{36x^4}{12x^4} = \frac{36}{12} \cdot \frac{x^4}{x^4} = 3 \cdot 1 = 3.
$$[/tex]
Step 2: Divide the second term
Again, divide the coefficients and subtract the exponents (using the property [tex]$x^a/x^b = x^{a-b}$[/tex]):
[tex]$$
\frac{12x^8}{12x^4} = \frac{12}{12} \cdot \frac{x^8}{x^4} = 1 \cdot x^{8-4} = x^4.
$$[/tex]
Step 3: Combine the results
Now, add the two parts together:
[tex]$$
3 + x^4.
$$[/tex]
Thus, the result of the division is
[tex]$$\boxed{3 + x^4}.$$[/tex]
