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Divide and simplify:
[tex]$
\frac{2 x^2}{3} \div \frac{x^3}{9}
$[/tex]

A. [tex]\(\frac{6}{x}\)[/tex]

B. [tex]\(\frac{x^5}{13}\)[/tex]

C. [tex]\(\frac{6 x^2}{x^3}\)[/tex]

D. [tex]\(\frac{x}{6}\)[/tex]

Sagot :

To solve and simplify the expression [tex]\(\frac{2 x^2}{3} \div \frac{x^3}{9}\)[/tex]:

1. Understand the problem: We need to divide one fraction by another.

2. Reciprocal of the Divisor: Dividing by a fraction is the same as multiplying by its reciprocal. So, instead of dividing by [tex]\(\frac{x^3}{9}\)[/tex], we can multiply by its reciprocal, [tex]\(\frac{9}{x^3}\)[/tex].

[tex]\[ \frac{2 x^2}{3} \div \frac{x^3}{9} = \frac{2 x^2}{3} \times \frac{9}{x^3} \][/tex]

3. Multiply the Fractions: To multiply two fractions, multiply their numerators and their denominators:

[tex]\[ \frac{2 x^2 \times 9}{3 \times x^3} = \frac{18 x^2}{3 x^3} \][/tex]

4. Simplify the Fraction:
- Simplify the numerical part: [tex]\(\frac{18}{3} = 6\)[/tex]
- Simplify the variable part: [tex]\(\frac{x^2}{x^3} = \frac{1}{x^{3-2}} = \frac{1}{x}\)[/tex]

So, the simplified fraction is:

[tex]\[ \frac{18 x^2}{3 x^3} = 6 \times \frac{1}{x} = \frac{6}{x} \][/tex]

Therefore, the final answer is:

[tex]\(\boxed{\frac{6}{x}}\)[/tex]
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