High School

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When [tex]$36x^4 + 12x^3$[/tex] is divided by [tex]$12x^4$[/tex], the result is:

A. [tex]3 + 12x^8[/tex]
B. [tex]3 + 12x^8[/tex]
C. [tex]3 + x^4[/tex]
D. [tex]3x + x^2[/tex]

Answer :

We want to simplify the expression

[tex]$$
\frac{36x^4 + 12x^3}{12x^4}.
$$[/tex]

Follow these steps:

1. Write the fraction as the sum of two separate fractions:

[tex]$$
\frac{36x^4}{12x^4} + \frac{12x^3}{12x^4}.
$$[/tex]

2. Simplify the first term:

[tex]$$
\frac{36x^4}{12x^4} = \frac{36}{12} = 3.
$$[/tex]

3. Simplify the second term by canceling the common factors:

[tex]$$
\frac{12x^3}{12x^4} = \frac{12}{12} \cdot \frac{x^3}{x^4} = 1 \cdot \frac{1}{x} = \frac{1}{x}.
$$[/tex]

4. Combine the two simplified terms:

[tex]$$
3 + \frac{1}{x}.
$$[/tex]

Thus, the final result of the division is

[tex]$$
3 + \frac{1}{x}.
$$[/tex]

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