Solve (2/x^6)/ x/3-3x

Question

Simplify the expression

\frac{2 - 9 x ^{8}}{3 x ^{7}}

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x = 0

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x_{1} = - \frac{8 1458}{3}, x_{2} = \frac{8 1458}{3}

Alternative Form

x_{1} \approx - 0.828607, x_{2} \approx 0.828607

Evaluate

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

To find the roots of the expression,set the expression equal to 0

\frac{\frac{\frac{2}{x ^{6}}}{x}}{3} - 3 x = 0

Find the domain

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\frac{\frac{\frac{2}{x ^{6}}}{x}}{3} - 3 x = 0, x \neq = 0

Calculate

\frac{\frac{\frac{2}{x ^{6}}}{x}}{3} - 3 x = 0

Divide the terms

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\frac{\frac{2}{x ^{7}}}{3} - 3 x = 0

Divide the terms

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\frac{2}{3 x ^{7}} - 3 x = 0

Subtract the terms

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\frac{2 - 9 x ^{8}}{3 x ^{7}} = 0

Cross multiply

2 - 9 x^{8} = 3 x^{7} \times 0

Simplify the equation

2 - 9 x^{8} = 0

Rewrite the expression

- 9 x^{8} = - 2

Change the signs on both sides of the equation

9 x^{8} = 2

Divide both sides

\frac{9 x ^{8}}{9} = \frac{2}{9}

Divide the numbers

x^{8} = \frac{2}{9}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm 8 \frac{2}{9}

Simplify the expression

More Steps

x = \pm \frac{8 1458}{3}

Separate the equation into 2 possible cases

x = \frac{8 1458}{3} x = - \frac{8 1458}{3}

Check if the solution is in the defined range

x = \frac{8 1458}{3} x = - \frac{8 1458}{3}, x \neq = 0

Find the intersection of the solution and the defined range

x = \frac{8 1458}{3} x = - \frac{8 1458}{3}

Solution

x_{1} = - \frac{8 1458}{3}, x_{2} = \frac{8 1458}{3}

Alternative Form

x_{1} \approx - 0.828607, x_{2} \approx 0.828607

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