What is 2x(xsqrt(x-1))(x/(2sqrt(x-1))+sqrt(x-1)) ?

The solution to 2x(xsqrt(x-1))(x/(2sqrt(x-1))+sqrt(x-1)) is x^2(3x-2)

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simplify 2x(xsqrt(x-1))(x/(2sqrt(x-1))+sqrt(x-1))

simplify

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

x^{2} (3 x - 2)

Solution steps

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

Join

\frac{x}{2 x - 1} + x - 1 : \frac{3 x - 2}{2 x - 1}

= 2 xx x - 1 \frac{3 x - 2}{2 x - 1}

Apply exponent rule:

aa = a^{2}

xx = x^{2}

= 2 x^{2} x - 1 \frac{3 x - 2}{2 x - 1}

= 2 x^{2} \frac{3 x - 2}{2 x - 1} x - 1

Apply the fraction rule:

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

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

Cancel the common factor:

2

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

Cancel the common factor:

x - 1

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

(\frac{1}{3}) e^{- 3 (\frac{1}{3})}

1296

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

(\frac{3}{5})^{2}

(\frac{3}{5})^{3}

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