Divide. Write your answer in simplest form. 8s/9s^2 - 15s + 4 ÷ 3/5s + 2 ______

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Rewrite division as multiplication: Write the division of the two fractions as a multiplication by the reciprocal of the second fraction. We have: (8s/(9s^2 - 15s + 4)) ÷ (3/(5s + 2)) This can be rewritten as: (8s/(9s^2 - 15s + 4)) * ((5s + 2)/3)Factor quadratic expression: Factor the quadratic expression in the denominator of the first fraction if possible. The quadratic expression is 9s^2 - 15s + 4. We need to check if it can be factored. Factoring attempt: (3s - 4)(3s - 1) = 9s^2 - 3s - 12s + 4 = 9s^2 - 15s + 4 So, the factored form is correct. The first fraction becomes: (8s/((3s - 4)(3s - 1)))Multiply numerators and denominators: Multiply the numerators and the denominators of the two fractions. We have: (8s/((3s - 4)(3s - 1))) * ((5s + 2)/3) Multiplying the numerators: 8s * (5s + 2) = 40s^2 + 16s Multiplying the denominators: (3s - 4)(3s - 1) * 3 = 3(3s - 4)(3s - 1) The expression becomes: (40s^2 + 16s)/(3(3s - 4)(3s - 1))Simplify expression: Simplify the expression if possible. We look for common factors in the numerator and the denominator. There are no common factors between 40s^2 + 16s and (3s - 4)(3s - 1). So, the expression is already in its simplest form.

Divide. Write your answer in simplest form. $\newline$ $\frac{8s}{9s^2 - 15s + 4} \div \frac{3}{5s + 2}$

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Divide. Write your answer in simplest form. $\newline$ $\frac{8s}{9s^2 - 15s + 4} \div \frac{3}{5s + 2}$