Divide. Simplify your answer. 7gh/19h^2 ÷ 15g^2 ______

Rewrite as multiplication: Rewrite the division as a multiplication by taking the reciprocal of the second fraction. So, (7gh/19h^2) ÷ (15g^2) becomes (7gh/19h^2) × (1/15g^2).Multiply numerators and denominators: Multiply the numerators and then multiply the denominators. So, (7gh/19h^2) × (1/15g^2) = (7gh × 1)/(19h^2 × 15g^2).Cancel out common factors: Simplify the expression by canceling out common factors. The g in the numerator and one g in the denominator cancel out, leaving us with (7h × 1)/(19h^2 × 15g). Similarly, h in the numerator and one h in the denominator cancel out, giving us (7 × 1)/(19h × 15g).Simplify further: Simplify the fraction further by multiplying the denominators. So, (7 × 1)/(19h × 15g) = 7/(19 × 15gh).Multiply denominators: Multiply the numbers in the denominator to get the final simplified form. So, 7/(19 × 15gh) = 7/(285gh).Check for simplification: Check for any further simplification. Since there are no common factors between 7 and 285gh, the fraction is already in its simplest form.

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Algebra 1

Multiply and divide rational expressions

Full solution

Q. Divide. Simplify your answer.

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\frac{7gh}{19h^2} \div \frac{15g^2}{1}

Rewrite as multiplication: Rewrite the division as a multiplication by taking the reciprocal of the second fraction. So, $(\frac{7gh}{19h^2}) \div (15g^2)$ becomes $(\frac{7gh}{19h^2}) \times (\frac{1}{15g^2})$ .
Multiply numerators and denominators: Multiply the numerators and then multiply the denominators. So, $(\frac{7gh}{19h^2}) \times (\frac{1}{15g^2}) = \frac{7gh \times 1}{19h^2 \times 15g^2}$ .
Cancel out common factors: Simplify the expression by canceling out common factors. The $g$ in the numerator and one $g$ in the denominator cancel out, leaving us with $(7h \times 1)/(19h^2 \times 15g)$ . Similarly, $h$ in the numerator and one $h$ in the denominator cancel out, giving us $(7 \times 1)/(19h \times 15g)$ .
Simplify further: Simplify the fraction further by multiplying the denominators. So, $(7 \times 1)/(19h \times 15g) = 7/(19 \times 15gh)$ .
Multiply denominators: Multiply the numbers in the denominator to get the final simplified form. So, $\frac{7}{19 \times 15gh} = \frac{7}{285gh}.$
Check for simplification: Check for any further simplification. Since there are no common factors between $7$ and $285gh$ , the fraction is already in its simplest form.