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

The solution to expand (2x-3/x)^2 is (4x^4-12x^2+9)/(x^2)

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expand (2x-3/x)^2

expand

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

\frac{4 x ^{4} - 12 x ^{2} + 9}{x ^{2}}

Solution steps

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

Apply Perfect Square Formula:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

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

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

Simplify

(2 x)^{2} - 2 \cdot 2 x \frac{3}{x} + (\frac{3}{x})^{2} : \frac{4 x ^{4} - 12 x ^{2} + 9}{x ^{2}}

= \frac{4 x ^{4} - 12 x ^{2} + 9}{x ^{2}}

\frac{3 x ^{4} - 7 x ^{3} + 6 k x ^{2} + 12 k ^{2} x - 2}{( x - 1 ) ^{2}}

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

3 (3 x^{2} - 5 x - 2)^{2}

(1 + i)^{5}

What is expand (2x-3/x)^2 ?
The solution to expand (2x-3/x)^2 is (4x^4-12x^2+9)/(x^2)