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

The solution to expand ((2x+3)^3)/(2x^2) is 4x+18+(27)/x+(27)/(2x^2)

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

expand

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

4 x + 18 + \frac{27}{x} + \frac{27}{2 x ^{2}}

Solution steps

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

(2 x + 3)^{3} = 8 x^{3} + 36 x^{2} + 54 x + 27

= \frac{8 x ^{3} + 36 x ^{2} + 54 x + 27}{2 x ^{2}}

Apply the fraction rule:

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

\frac{8 x ^{3} + 36 x ^{2} + 54 x + 27}{2 x ^{2}} = \frac{8 x ^{3}}{2 x ^{2}} + \frac{36 x ^{2}}{2 x ^{2}} + \frac{54 x}{2 x ^{2}} + \frac{27}{2 x ^{2}}

= \frac{8 x ^{3}}{2 x ^{2}} + \frac{36 x ^{2}}{2 x ^{2}} + \frac{54 x}{2 x ^{2}} + \frac{27}{2 x ^{2}}

Cancel

\frac{8 x ^{3}}{2 x ^{2}} : 4 x

= 4 x + \frac{36 x ^{2}}{2 x ^{2}} + \frac{54 x}{2 x ^{2}} + \frac{27}{2 x ^{2}}

Cancel

\frac{36 x ^{2}}{2 x ^{2}} : 18

= 4 x + 18 + \frac{54 x}{2 x ^{2}} + \frac{27}{2 x ^{2}}

Cancel

\frac{54 x}{2 x ^{2}} : \frac{27}{x}

= 4 x + 18 + \frac{27}{x} + \frac{27}{2 x ^{2}}

A (- 1, - 2) B (3, - 2)

\frac{( 2 + 3 x ) ^{2}}{4}

(5 x + 1 \circ x^{2} - 5) (- 4)

(e^{2 x} + 2 x e^{2 x}) (4 x e^{2 x})

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

What is expand ((2x+3)^3)/(2x^2) ?
The solution to expand ((2x+3)^3)/(2x^2) is 4x+18+(27)/x+(27)/(2x^2)