What is x((x^2}{24}-x+6)(32/3-\frac{8x)/9) ?

The solution to x((x^2}{24}-x+6)(32/3-\frac{8x)/9) is (x(x^2-24x+144)(12-x))/(27)

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simplify x((x^2}{24}-x+6)(32/3-\frac{8x)/9)

simplify

x (\frac{x ^{2}}{24} - x + 6) (\frac{32}{3} - \frac{8 x}{9})

\frac{x ( x ^{2} - 24 x + 144 ) ( 12 - x )}{27}

Solution steps

x (\frac{x ^{2}}{24} - x + 6) (\frac{32}{3} - \frac{8 x}{9})

Simplify

\frac{x ^{2}}{24} - x + 6 : \frac{x ^{2} - 24 x + 144}{24}

= x \frac{x ^{2} - 24 x + 144}{24} (\frac{32}{3} - \frac{8 x}{9})

Apply the fraction rule:

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

= \frac{x ( x ^{2} - 24 x + 144 ) ( \frac{32}{3} - \frac{8 x}{9} )}{24}

Simplify

x (x^{2} - 24 x + 144) (\frac{32}{3} - \frac{8 x}{9}) : \frac{x ( x ^{2} - 24 x + 144 ) ( 96 - 8 x )}{9}

= \frac{\frac{x ( x ^{2} - 24 x + 144 ) ( 96 - 8 x )}{9}}{24}

Apply the fraction rule:

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

= \frac{x ( x ^{2} - 24 x + 144 ) ( 96 - 8 x )}{9 \cdot 24}

Multiply the numbers:

9 \cdot 24 = 216

= \frac{x ( x ^{2} - 24 x + 144 ) ( 96 - 8 x )}{216}

Factor

96 - 8 x : 8 (12 - x)

= \frac{x ( x ^{2} - 24 x + 144 ) \cdot 8 ( 12 - x )}{216}

Factor the number:

216 = 8 \cdot 27

= \frac{x ( x ^{2} - 24 x + 144 ) \cdot 8 ( 12 - x )}{8 \cdot 27}

Cancel the common factor:

8

= \frac{x ( x ^{2} - 24 x + 144 ) ( 12 - x )}{27}

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

What is x((x^2}{24}-x+6)(32/3-\frac{8x)/9) ?
The solution to x((x^2}{24}-x+6)(32/3-\frac{8x)/9) is (x(x^2-24x+144)(12-x))/(27)