Solve (4n^322n^2-12n)/(n^6)

Simplify the expression

\frac{88 n ^{4} - 12}{n ^{5}}

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n = 0

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- \frac{12}{n ^{5}} + \frac{88}{n}

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n_{1} = - \frac{4 31944}{22}, n_{2} = \frac{4 31944}{22}

Alternative Form

n_{1} \approx - 0.60768, n_{2} \approx 0.60768

Evaluate

\frac{4 n ^{3} \times 22 n ^{2} - 12 n}{n ^{6}}

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

\frac{4 n ^{3} \times 22 n ^{2} - 12 n}{n ^{6}} = 0

The only way a power can not be 0 is when the base not equals 0

\frac{4 n ^{3} \times 22 n ^{2} - 12 n}{n ^{6}} = 0, n \neq = 0

Calculate

\frac{4 n ^{3} \times 22 n ^{2} - 12 n}{n ^{6}} = 0

Multiply

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\frac{88 n ^{5} - 12 n}{n ^{6}} = 0

Divide the terms

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\frac{88 n ^{4} - 12}{n ^{5}} = 0

Cross multiply

88 n^{4} - 12 = n^{5} \times 0

Simplify the equation

88 n^{4} - 12 = 0

Move the constant to the right side

88 n^{4} = 12

Divide both sides

\frac{88 n ^{4}}{88} = \frac{12}{88}

Divide the numbers

n^{4} = \frac{12}{88}

Cancel out the common factor 4

n^{4} = \frac{3}{22}

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

n = \pm 4 \frac{3}{22}

Simplify the expression

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n = \pm \frac{4 31944}{22}

Separate the equation into 2 possible cases

n = \frac{4 31944}{22} n = - \frac{4 31944}{22}

Check if the solution is in the defined range

n = \frac{4 31944}{22} n = - \frac{4 31944}{22}, n \neq = 0

Find the intersection of the solution and the defined range

n = \frac{4 31944}{22} n = - \frac{4 31944}{22}

Solution

n_{1} = - \frac{4 31944}{22}, n_{2} = \frac{4 31944}{22}

Alternative Form

n_{1} \approx - 0.60768, n_{2} \approx 0.60768

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