Solve (x^(2)-4x-32)/(x^(2) 12x^32) / (5x)/(x^(2) 64)

Question

Simplify the expression

\frac{8 x ^{2} - 32 x - 256}{15 x ^{4}}

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x = 0

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x_{1} = - 4, x_{2} = 8

Evaluate

\frac{x ^{2} - 4 x - 32}{x ^{2} \times 12 x ^{3} \times 2} \div \frac{5 x}{x ^{2} \times 64}

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

\frac{x ^{2} - 4 x - 32}{x ^{2} \times 12 x ^{3} \times 2} \div \frac{5 x}{x ^{2} \times 64} = 0

Find the domain

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\frac{x ^{2} - 4 x - 32}{x ^{2} \times 12 x ^{3} \times 2} \div \frac{5 x}{x ^{2} \times 64} = 0, x \neq = 0

Calculate

\frac{x ^{2} - 4 x - 32}{x ^{2} \times 12 x ^{3} \times 2} \div \frac{5 x}{x ^{2} \times 64} = 0

Multiply

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\frac{x ^{2} - 4 x - 32}{24 x ^{5}} \div \frac{5 x}{x ^{2} \times 64} = 0

Use the commutative property to reorder the terms

\frac{x ^{2} - 4 x - 32}{24 x ^{5}} \div \frac{5 x}{64 x ^{2}} = 0

Divide the terms

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\frac{x ^{2} - 4 x - 32}{24 x ^{5}} \div \frac{5}{64 x} = 0

Divide the terms

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\frac{8 ( x ^{2} - 4 x - 32 )}{15 x ^{4}} = 0

Cross multiply

8 (x^{2} - 4 x - 32) = 15 x^{4} \times 0

Simplify the equation

8 (x^{2} - 4 x - 32) = 0

Rewrite the expression

x^{2} - 4 x - 32 = 0

Factor the expression

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(x - 8) (x + 4) = 0

When the product of factors equals 0,at least one factor is 0

x - 8 = 0 x + 4 = 0

Solve the equation for x

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x = 8 x + 4 = 0

Solve the equation for x

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x = 8 x = - 4

Check if the solution is in the defined range

x = 8 x = - 4, x \neq = 0

Find the intersection of the solution and the defined range

x = 8 x = - 4

Solution

x_{1} = - 4, x_{2} = 8

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