Divide. Write your answer in simplest form. v/2v + 3 ÷ 5v - 1/v^2 - 4 ______

Write Problem: Write the original problem and identify the expressions to be divided. We have the expression v/(2v + 3) ÷ (5v - 1)/(v^2 - 4). Rewrite the division as multiplication by the reciprocal of the second fraction. The expression becomes v/(2v + 3) * (v^2 - 4)/(5v - 1).Rewrite Division: Factor the denominator of the second fraction if possible. Notice that v^2 - 4 is a difference of squares and can be factored into (v + 2)(v - 2). So, the expression becomes v/(2v + 3) * (v + 2)(v - 2)/(5v - 1).Factor Denominator: Multiply the numerators and the denominators. Now, multiply the numerators together and the denominators together. The expression becomes (v * (v + 2)(v - 2))/((2v + 3)(5v - 1)).Multiply Numerators: Simplify the expression if possible. Look for common factors in the numerator and the denominator that can be canceled out. In this case, there are no common factors to cancel, so the expression is already in its simplest form. The simplified expression is (v(v + 2)(v - 2))/((2v + 3)(5v - 1)).

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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{v}{2v + 3} \div \frac{5v - 1}{v^2 - 4}

Write Problem: Write the original problem and identify the expressions to be divided. $\newline$ We have the expression $\frac{v}{2v + 3} \div \frac{5v - 1}{v^2 - 4}$ . $\newline$ Rewrite the division as multiplication by the reciprocal of the second fraction. $\newline$ The expression becomes $\frac{v}{2v + 3} \times \frac{v^2 - 4}{5v - 1}$ .
Rewrite Division: Factor the denominator of the second fraction if possible. $\newline$ Notice that $v^2 - 4$ is a difference of squares and can be factored into $(v + 2)(v - 2)$ . $\newline$ So, the expression becomes $\frac{v}{2v + 3} \times \frac{(v + 2)(v - 2)}{5v - 1}.$
Factor Denominator: Multiply the numerators and the denominators. $\newline$ Now, multiply the numerators together and the denominators together. $\newline$ The expression becomes $(v \times (v + 2)(v - 2))/((2v + 3)(5v - 1))$ .
Multiply Numerators: Simplify the expression if possible. $\newline$ Look for common factors in the numerator and the denominator that can be canceled out. $\newline$ In this case, there are no common factors to cancel, so the expression is already in its simplest form. $\newline$ The simplified expression is $(v(v + 2)(v - 2))/((2v + 3)(5v - 1))$ .