Which of the following is equivalent to (((3x)/(2)))/(((3)/(x)+2)) ? Choose 1 answer: (A) (9)/(4) (B) (3x+2)/(9) (C) (9x^(2))/(4) (D) (3x^(2))/(6+4x)

Simplify denominator of complex fraction: Simplify the denominator of the complex fraction. The denominator is (3/x) + 2. To combine these terms, we need a common denominator, which is x. So we rewrite the terms with a common denominator: (3/x) + 2 = (3/x) + (2x/x)Combine terms in denominator: Combine the terms in the denominator. Now that we have a common denominator, we can combine the terms: (3/x) + (2x/x) = (3 + 2x)/xRewrite complex fraction as division: Rewrite the complex fraction as a division. The original expression (((3x)/(2)))/(((3)/(x)+2)) can now be written as: (3x/2) ÷ ((3 + 2x)/x)Divide by fraction by multiplying by reciprocal: Divide by a fraction by multiplying by its reciprocal. To divide by a fraction, we multiply by its reciprocal. The reciprocal of ((3 + 2x)/x) is (x/(3 + 2x)): (3x/2) * (x/(3 + 2x))Simplify expression: Simplify the expression. Now we multiply the numerators and the denominators: (3x * x) / (2 * (3 + 2x)) This simplifies to: (3x^2) / (6 + 4x)

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Which of the following is equivalent to
(((3x)/(2)))/(((3)/(x)+2)) ?
Choose 1 answer:
(A)
(9)/(4)
(B)
(3x+2)/(9)
(C)
(9x^(2))/(4)
(D)
(3x^(2))/(6+4x)

Which of the following is equivalent to $\frac{\left(\frac{3 x}{2}\right)}{\left(\frac{3}{x}+2\right)}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{9}{4}$ $\newline$ (B) $\frac{3 x+2}{9}$ $\newline$ (C) $\frac{9 x^{2}}{4}$ $\newline$ (D) $\frac{3 x^{2}}{6+4 x}$

View step-by-step help

Home

Math Problems

Grade 7

Identify equivalent linear expressions I

Full solution

Q. Which of the following is equivalent to

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

\newline

Choose

1

answer:

\newline

(A)

\frac{9}{4}

\newline

(B)

\frac{3 x+2}{9}

\newline

(C)

\frac{9 x^{2}}{4}

\newline

(D)

\frac{3 x^{2}}{6+4 x}

Simplify denominator of complex fraction: Simplify the denominator of the complex fraction. $\newline$ The denominator is $(\frac{3}{x}) + 2$ . To combine these terms, we need a common denominator, which is $x$ . So we rewrite the terms with a common denominator: $\newline$ $(\frac{3}{x}) + 2 = (\frac{3}{x}) + (\frac{2x}{x})$
Combine terms in denominator: Combine the terms in the denominator. $\newline$ Now that we have a common denominator, we can combine the terms: $\newline$ $(\frac{3}{x}) + (\frac{2x}{x}) = \frac{3 + 2x}{x}$
Rewrite complex fraction as division: Rewrite the complex fraction as a division. $\newline$ The original expression $\frac{\frac{3x}{2}}{\frac{3}{x}+2}$ can now be written as: $\newline$ $\frac{3x}{2}$ $\div$ $\frac{3 + 2x}{x}$
Divide by fraction by multiplying by reciprocal: Divide by a fraction by multiplying by its reciprocal. $\newline$ To divide by a fraction, we multiply by its reciprocal. The reciprocal of $(\frac{3 + 2x}{x})$ is $(\frac{x}{3 + 2x})$ : $\newline$ $(\frac{3x}{2}) \cdot (\frac{x}{3 + 2x})$
Simplify expression: Simplify the expression. $\newline$ Now we multiply the numerators and the denominators: $\newline$ $(3x \times x) / (2 \times (3 + 2x))$ $\newline$ This simplifies to: $\newline$ $(3x^2) / (6 + 4x)$