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

The solution to expand ((x-2)(x+2)(x+3/2))/(x-1) is (2x^3-8x+3x^2-12)/(2x-2)

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

expand

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

\frac{2 x ^{3} - 8 x + 3 x ^{2} - 12}{2 x - 2}

Solution steps

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

Join

x + \frac{3}{2} : \frac{2 x + 3}{2}

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

Multiply

(x - 2) (x + 2) \frac{x \cdot 2 + 3}{2} : \frac{2 x ^{3} - 8 x + 3 x ^{2} - 12}{2}

= \frac{\frac{2 x ^{3} - 8 x + 3 x ^{2} - 12}{2}}{x - 1}

Apply the fraction rule:

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

= \frac{2 x ^{3} - 8 x + 3 x ^{2} - 12}{2 ( x - 1 )}

Expand

2 (x - 1) : 2 x - 2

= \frac{2 x ^{3} - 8 x + 3 x ^{2} - 12}{2 x - 2}

6 - x ((- 2 - x) (5 - x))

256 e^{4 x} \cdot (10 x^{6} - 6 x^{5})

(- e^{- t} + e^{- 2 t}) u (- t)

\frac{( s + 1 ) e ^{5} s}{( s ^{2} + 2 s + 10 )}

\frac{( x ^{2 (2 n + 1)} + 3 ^{2 n + 1} )}{7}

What is expand ((x-2)(x+2)(x+3/2))/(x-1) ?
The solution to expand ((x-2)(x+2)(x+3/2))/(x-1) is (2x^3-8x+3x^2-12)/(2x-2)