Divide. Write your answer in simplest form. 2g - 3/g^2 - 1 ÷ g^2/2g + 3 ______

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Rewrite as Multiplication: Rewrite the division problem as a multiplication problem by taking the reciprocal of the second fraction. (2g - 3)/(g^2 - 1) ÷ (g^2)/(2g + 3) can be rewritten as (2g - 3)/(g^2 - 1) * (2g + 3)/g^2.Factor Denominator: Factor the denominator of the first fraction if possible. The denominator g^2 - 1 is a difference of squares and can be factored into (g - 1)(g + 1). So, the expression becomes (2g - 3)/((g - 1)(g + 1)) * (2g + 3)/g^2.Multiply Numerators and Denominators: Multiply the numerators and the denominators of the two fractions. The expression becomes ((2g - 3) * (2g + 3))/((g - 1)(g + 1) * g^2).Expand Numerator: Expand the numerator of the resulting fraction. The numerator (2g - 3) * (2g + 3) is a product of two binomials that are conjugates of each other, which results in a difference of squares. So, (2g - 3) * (2g + 3) = (2g)^2 - (3)^2 = 4g^2 - 9. The expression becomes (4g^2 - 9)/((g - 1)(g + 1) * g^2).Simplify Expression: Simplify the expression by canceling out common factors if there are any. There are no common factors between the numerator 4g^2 - 9 and the denominator (g - 1)(g + 1) * g^2. So, the expression remains (4g^2 - 9)/((g - 1)(g + 1) * g^2).Rewrite Denominator: Rewrite the denominator to make it clear what can be simplified. The denominator is (g - 1)(g + 1) * g^2, which can be rewritten as g^2(g - 1)(g + 1). The expression becomes (4g^2 - 9)/(g^2(g - 1)(g + 1)).Cancel Common Term: Cancel out the common g^2 term from the numerator and the denominator. After canceling out g^2, the expression simplifies to (4 - 9/g^2)/((g - 1)(g + 1)).

Divide. Write your answer in simplest form. $\newline$ $\frac{2g - 3}{g^2 - 1} \div \frac{g^2}{2g + 3}$

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Divide. Write your answer in simplest form. $\newline$ $\frac{2g - 3}{g^2 - 1} \div \frac{g^2}{2g + 3}$