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

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

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

expand

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

\frac{1}{4} - \frac{1}{2 x} + \frac{1}{4 x ^{2}}

Solution steps

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

Apply exponent rule:

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

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

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(2 x)^{2} = 2^{2} x^{2}

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

(x - 1)^{2} = x^{2} - 2 x + 1

= \frac{x ^{2} - 2 x + 1}{2 ^{2} x ^{2}}

2^{2} = 4

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

Apply the fraction rule:

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

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

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

Cancel

\frac{x ^{2}}{4 x ^{2}} : \frac{1}{4}

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

Cancel

\frac{2 x}{4 x ^{2}} : \frac{1}{2 x}

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

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