What is expand (((3x)/2))/((3/x+2)) ?

The solution to expand (((3x)/2))/((3/x+2)) is (3x^2)/(6+4x)

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expand (((3x)/2))/((3/x+2))

expand

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

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

Solution steps

\frac{\frac{3 x}{2}}{\frac{3}{x} + 2}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{3 x}{2 ( \frac{3}{x} + 2 )}

Join

\frac{3}{x} + 2 : \frac{3 + 2 x}{x}

= \frac{3 x}{2 \cdot \frac{2 x + 3}{x}}

Multiply

2 \cdot \frac{3 + 2 x}{x} : \frac{6 + 4 x}{x}

= \frac{3 x}{\frac{6 + 4 x}{x}}

Apply the fraction rule:

\frac{a}{\frac{b}{c}} = \frac{a \cdot c}{b}

= \frac{3 xx}{6 + 4 x}

3 xx = 3 x^{2}

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

(x + 5) + (x + 5) + (3 x - 2)

(v + 1) (v d y + y d v)

\frac{1}{( s + 7 ) ( s - 5 ) ( s + 12 )}

(x + \frac{1}{x})^{2} (x + \frac{1}{x})

\frac{d ^{2}}{d x ^{2}} ((x) (5 \cdot x^{3} - 2 \cdot x^{2} + 2 \cdot x))

What is expand (((3x)/2))/((3/x+2)) ?
The solution to expand (((3x)/2))/((3/x+2)) is (3x^2)/(6+4x)