Divide. Simplify your answer. 8x^2/12w^2x ÷ 19wx ______

Rewrite as multiplication: Rewrite the division as a multiplication by taking the reciprocal of the second fraction. So, (8x^2/12w^2x) ÷ (19wx) becomes (8x^2/12w^2x) × (1/19wx).Simplify first fraction: Simplify the first fraction by canceling common factors. The common factor x can be canceled from the numerator and denominator, and the numbers 8 and 12 can be reduced by dividing both by their greatest common divisor, which is 4. So, (8x^2/12w^2x) simplifies to (2x/3w^2).Multiply by reciprocal: Multiply the simplified first fraction by the reciprocal of the second fraction. So, (2x/3w^2) × (1/19wx) becomes (2x/3w^2) × (1/19wx) = (2x * 1)/(3w^2 * 19wx).Simplify resulting fraction: Simplify the resulting fraction by canceling common factors. The common factor x can be canceled from the numerator and denominator. So, (2x * 1)/(3w^2 * 19wx) simplifies to (2)/(3w^2 * 19w) = 2/(57w^3).

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Algebra 1

Multiply and divide rational expressions

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Q. Divide. Simplify your answer.

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\frac{8x^2}{12w^2x} \div 19wx

Rewrite as multiplication: Rewrite the division as a multiplication by taking the reciprocal of the second fraction. So, $(\frac{8x^2}{12w^2x}) \div (\frac{19wx}{1})$ becomes $(\frac{8x^2}{12w^2x}) \times (\frac{1}{19wx})$ .
Simplify first fraction: Simplify the first fraction by canceling common factors. The common factor $x$ can be canceled from the numerator and denominator, and the numbers $8$ and $12$ can be reduced by dividing both by their greatest common divisor, which is $4$ . So, $(\frac{8x^2}{12w^2x})$ simplifies to $(\frac{2x}{3w^2})$ .
Multiply by reciprocal: Multiply the simplified first fraction by the reciprocal of the second fraction. So, $(\frac{2x}{3w^2}) \times (\frac{1}{19wx})$ becomes $(\frac{2x}{3w^2}) \times (\frac{1}{19wx}) = (\frac{2x \times 1}{3w^2 \times 19wx})$ .
Simplify resulting fraction: Simplify the resulting fraction by canceling common factors. The common factor $x$ can be canceled from the numerator and denominator. So, $(2x \times 1)/(3w^2 \times 19wx)$ simplifies to $(2)/(3w^2 \times 19w) = 2/(57w^3)$ .