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Divide. Simplify your answer. $\newline$ $\frac{3x}{17xy^2} \div 11y^2$

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Multiply and divide rational expressions

Full solution

Q. Divide. Simplify your answer.

\newline

\frac{3x}{17xy^2} \div 11y^2

Rewrite as multiplication: Rewrite the division as a multiplication by taking the reciprocal of the divisor. So, $\frac{3x}{17xy^2} \div \frac{11y^2}{1}$ becomes $\frac{3x}{17xy^2} \times \frac{1}{11y^2}.$
Multiply numerators and denominators: Multiply the numerators and then multiply the denominators. So, $(3x \times 1) / (17xy^2 \times 11y^2)$ becomes $3x / (17x \times 11 \times y^2 \times y^2)$ .
Simplify by canceling factors: Simplify the expression by canceling out common factors. The $x$ in the numerator and one $x$ in the denominator cancel out, and $y^2$ in the denominator is squared, so it becomes $y^4$ . The expression now is $\frac{3}{17 \times 11 \times y^4}$ .
Multiply constants in denominator: Multiply the constants in the denominator. So, $17 \times 11$ becomes $187$ . The expression now is $\frac{3}{187y^4}$ .
Write final answer: Write the final answer in the simplest form. So, the simplified result is $\frac{3}{187y^4}$ .

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