What is expand (3(2x-1)^2)/(2x) ?

The solution to expand (3(2x-1)^2)/(2x) is 6x-6+3/(2x)

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expand (3(2x-1)^2)/(2x)

expand

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

6 x - 6 + \frac{3}{2 x}

Solution steps

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

(2 x - 1)^{2} = 4 x^{2} - 4 x + 1

= \frac{3 ( 4 x ^{2} - 4 x + 1 )}{2 x}

Expand

3 (4 x^{2} - 4 x + 1) : 12 x^{2} - 12 x + 3

= \frac{12 x ^{2} - 12 x + 3}{2 x}

Apply the fraction rule:

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

\frac{12 x ^{2} - 12 x + 3}{2 x} = \frac{12 x ^{2}}{2 x} - \frac{12 x}{2 x} + \frac{3}{2 x}

= \frac{12 x ^{2}}{2 x} - \frac{12 x}{2 x} + \frac{3}{2 x}

Cancel

\frac{12 x ^{2}}{2 x} : 6 x

= 6 x - \frac{12 x}{2 x} + \frac{3}{2 x}

Cancel

\frac{12 x}{2 x} : 6

= 6 x - 6 + \frac{3}{2 x}

\frac{3 x ^{2} - 6 x + 2}{2 ( 4 - 3 y ^{2} + 2 y ^{3} - 4 y )}

\frac{2}{( x - 2 ) ( x - 5 )}

x d x + (y - 2 x) d y

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

\frac{- cot ( x ) csc ( x ) ( 1 + sec ( x ) ) - sec ( x ) tan ( x ) ( 1 + csc ( x ) )}{( 1 + sec ( x ) ) ^{2}}

What is expand (3(2x-1)^2)/(2x) ?
The solution to expand (3(2x-1)^2)/(2x) is 6x-6+3/(2x)