Divide. Write your answer in simplest form. 2x^3 - 3x^2/2x + 3 ÷ x^2/2x + 3 ______

Rewrite as multiplication: Rewrite the division problem as a multiplication problem by taking the reciprocal of the second fraction. (2x^3 - 3x^2)/(2x + 3) ÷ (x^2)/(2x + 3) becomes (2x^3 - 3x^2)/(2x + 3) * (2x + 3)/x^2.Identify expression after multiplication: Identify the expression after multiplying the numerators and the denominators. (2x^3 - 3x^2)/(2x + 3) * (2x + 3)/x^2 = (2x^3 - 3x^2) * (2x + 3)/(2x + 3) * x^2.Simplify by canceling common factors: Simplify the expression by canceling out the common factors in the numerator and the denominator. The (2x + 3) terms cancel each other out, leaving us with (2x^3 - 3x^2)/x^2.Divide terms in numerator: Divide each term in the numerator by x^2. 2x^3/x^2 - 3x^2/x^2 = 2x - 3.

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Divide. Write your answer in simplest form. $\newline$ $\frac{2x^3 - 3x^2}{2x + 3} \div \frac{x^2}{2x + 3}$

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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{2x^3 - 3x^2}{2x + 3} \div \frac{x^2}{2x + 3}

Rewrite as multiplication: Rewrite the division problem as a multiplication problem by taking the reciprocal of the second fraction. $\newline$ $(2x^3 - 3x^2)/(2x + 3) \div (x^2)/(2x + 3)$ becomes $(2x^3 - 3x^2)/(2x + 3) \times (2x + 3)/x^2$ .
Identify expression after multiplication: Identify the expression after multiplying the numerators and the denominators. $\newline$ $(2x^3 - 3x^2)/(2x + 3) \times (2x + 3)/x^2 = (2x^3 - 3x^2) \times (2x + 3)/(2x + 3) \times x^2$ .
Simplify by canceling common factors: Simplify the expression by canceling out the common factors in the numerator and the denominator. $\newline$ The $(2x + 3)$ terms cancel each other out, leaving us with $\frac{2x^3 - 3x^2}{x^2}$ .
Divide terms in numerator: Divide each term in the numerator by $x^2$ . $\newline$ $\frac{2x^3}{x^2} - \frac{3x^2}{x^2} = 2x - 3.$