Divide. Write your answer in simplest form. k^2 - 9/3k ÷ 8/7 ______

Write as multiplication problem: Write the division problem as a multiplication problem by taking the reciprocal of the second fraction. We have: (k^2 - 9)/(3k) ÷ 8/7. To divide by a fraction, we multiply by its reciprocal. So, we rewrite the expression as (k^2 - 9)/(3k) * 7/8.Factor numerator if possible: Factor the numerator of the first fraction if possible. The numerator k^2 - 9 is a difference of squares and can be factored into (k + 3)(k - 3). So, the expression becomes ((k + 3)(k - 3))/(3k) * 7/8.Multiply numerators and denominators: Multiply the numerators and the denominators of the two fractions. We multiply (k + 3)(k - 3) by 7 and 3k by 8. The expression becomes ((k + 3)(k - 3) * 7)/(3k * 8).Simplify expression: Simplify the expression by canceling out any common factors in the numerator and the denominator. There are no common factors between the numerator and the denominator, so the expression is already in its simplest form: ((k + 3)(k - 3) * 7)/(3k * 8).

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Algebra 2

Multiply and divide rational expressions

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Q. Divide. Write your answer in simplest form.

\newline

\frac{k^2 - 9}{3k} \div \frac{8}{7}

Write as multiplication problem: Write the division problem as a multiplication problem by taking the reciprocal of the second fraction. $\newline$ We have: $(k^2 - 9)/(3k) \div \frac{8}{7}$ . To divide by a fraction, we multiply by its reciprocal. So, we rewrite the expression as $(k^2 - 9)/(3k) \times \frac{7}{8}$ .
Factor numerator if possible: Factor the numerator of the first fraction if possible. $\newline$ The numerator $k^2 - 9$ is a difference of squares and can be factored into $(k + 3)(k - 3)$ . So, the expression becomes $\frac{(k + 3)(k - 3)}{3k} \times \frac{7}{8}$ .
Multiply numerators and denominators: Multiply the numerators and the denominators of the two fractions. We multiply $(k + 3)(k - 3)$ by $7$ and $3k$ by $8$ . The expression becomes $\frac{(k + 3)(k - 3) \times 7}{3k \times 8}$ .
Simplify expression: Simplify the expression by canceling out any common factors in the numerator and the denominator. $\newline$ There are no common factors between the numerator and the denominator, so the expression is already in its simplest form: $\frac{(k + 3)(k - 3) \times 7}{3k \times 8}.$