What is expand ((2x-1)/(x/2))^2 ?

The solution to expand ((2x-1)/(x/2))^2 is 16-(16)/x+4/(x^2)

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expand ((2x-1)/(x/2))^2

expand

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

16 - \frac{16}{x} + \frac{4}{x ^{2}}

Solution steps

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

\frac{2 x - 1}{\frac{x}{2}} = \frac{4 x - 2}{x}

= (\frac{4 x - 2}{x})^{2}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( 4 x - 2 ) ^{2}}{x ^{2}}

(4 x - 2)^{2} = 16 x^{2} - 16 x + 4

= \frac{16 x ^{2} - 16 x + 4}{x ^{2}}

Apply the fraction rule:

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

\frac{16 x ^{2} - 16 x + 4}{x ^{2}} = \frac{16 x ^{2}}{x ^{2}} - \frac{16 x}{x ^{2}} + \frac{4}{x ^{2}}

= \frac{16 x ^{2}}{x ^{2}} - \frac{16 x}{x ^{2}} + \frac{4}{x ^{2}}

Cancel

\frac{16 x ^{2}}{x ^{2}} : 16

= 16 - \frac{16 x}{x ^{2}} + \frac{4}{x ^{2}}

Cancel

\frac{16 x}{x ^{2}} : \frac{16}{x}

= 16 - \frac{16}{x} + \frac{4}{x ^{2}}

\frac{( - 24 x ^{2} + 12 x - 15 ) ( 4 x - 1 )}{16}

(2 x - 3 y) (\frac{1}{2}, \frac{3}{2})

(x + ln^{2} (x))^{3}

4 x y^{2} - 2 x y + \frac{( 4 x ^{2} y - x ^{2} - 5 ) d y}{d x}

x^{4} (δ (x - 2)) d x

What is expand ((2x-1)/(x/2))^2 ?
The solution to expand ((2x-1)/(x/2))^2 is 16-(16)/x+4/(x^2)