Divide. (3x/2)/(3/x+2)

Rewrite as division problem: Rewrite the complex fraction as a division problem. (3x/2) / (3/x + 2) can be rewritten as (3x/2) * (1 / (3/x + 2)).Simplify denominator: Simplify the expression in the denominator of the second fraction. To combine the terms in the denominator, find a common denominator, which is x. (3/x + 2) = (3 + 2x) / x.Rewrite with simplified denominator: Rewrite the original expression with the simplified denominator. Now the expression is (3x/2) * (1 / ((3 + 2x) / x)).Multiply the fractions: Multiply the two fractions. To multiply the fractions, we take the numerator of the first fraction and multiply it by the reciprocal of the second fraction. (3x/2) * (x / (3 + 2x)) = (3x * x) / (2 * (3 + 2x)).Simplify numerator: Simplify the multiplication in the numerator. Multiply 3x by x to get 3x^2. (3x^2) / (2 * (3 + 2x)) = 3x^2 / (6 + 4x).Check for further simplification: Check if the expression can be simplified further. The expression 3x^2 / (6 + 4x) cannot be simplified further because the numerator and denominator do not have common factors.

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Divide. $\left(\frac{3x}{2}\right)\div\left(\frac{3}{x}+2\right)$

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Algebra 1

Simplify radical expressions involving fractions

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Q. Divide.

\left(\frac{3x}{2}\right)\div\left(\frac{3}{x}+2\right)

Rewrite as division problem: Rewrite the complex fraction as a division problem. $\newline$ $(\frac{3x}{2}) / (\frac{3}{x} + 2)$ can be rewritten as $(\frac{3x}{2}) \cdot (\frac{1}{\frac{3}{x} + 2})$ .
Simplify denominator: Simplify the expression in the denominator of the second fraction. $\newline$ To combine the terms in the denominator, find a common denominator, which is $x$ . $\newline$ $(\frac{3}{x} + 2) = \frac{3 + 2x}{x}$ .
Rewrite with simplified denominator: Rewrite the original expression with the simplified denominator. $\newline$ Now the expression is $(\frac{3x}{2}) \times (\frac{1}{(\frac{3 + 2x}{x})})$ .
Multiply the fractions: Multiply the two fractions. $\newline$ To multiply the fractions, we take the numerator of the first fraction and multiply it by the reciprocal of the second fraction. $\newline$ $(\frac{3x}{2}) \times (\frac{x}{3 + 2x}) = \frac{3x \times x}{2 \times (3 + 2x)}$ .
Simplify numerator: Simplify the multiplication in the numerator. $\newline$ Multiply $3x$ by $x$ to get $3x^2$ . $\newline$ $\frac{3x^2}{2 \cdot (3 + 2x)} = \frac{3x^2}{6 + 4x}$ .
Check for further simplification: Check if the expression can be simplified further. $\newline$ The expression $\frac{3x^2}{6 + 4x}$ cannot be simplified further because the numerator and denominator do not have common factors.