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Divide. Simplify your answer. $\newline$ $\frac{17d^2}{20cd} \div 19c^2d$

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Multiply and divide rational expressions

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Q. Divide. Simplify your answer.

\newline

\frac{17d^2}{20cd} \div 19c^2d

Rewrite as multiplication: Rewrite the division as a multiplication by taking the reciprocal of the second fraction. So, $(\frac{17d^2}{20cd}) \div (19c^2d)$ becomes $(\frac{17d^2}{20cd}) \times (\frac{1}{19c^2d})$ .
Multiply numerators and denominators: Multiply the numerators and then multiply the denominators. So, $(\frac{17d^2}{20cd}) \times (\frac{1}{19c^2d}) = \frac{17d^2 \times 1}{20cd \times 19c^2d}$ .
Simplify by canceling factors: Simplify the expression by canceling out common factors. The $d$ in the numerator cancels with one $d$ in the denominator, and $c$ in the denominator cancels with one $c$ in the numerator. So, we get $\frac{17d}{20 \times 19c^2}$ .
Multiply constants in denominator: Multiply the constants in the denominator. So, $20 \times 19 = 380$ . The expression now is $(17d)/(380c^2)$ .
Write in simplest form: Write the answer in the simplest form. The fraction $(17d)/(380c^2)$ is already in its simplest form since $17$ and $380$ have no common factors other than $1$ .

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