Solve \frac{\left(-2x^{2} 6x 8\right)}{x^{2}-9}

Question

Simplify the expression

- \frac{96 x ^{3}}{x ^{2} - 9}

Evaluate

\frac{( - 2 x ^{2} \times 6 x \times 8 )}{x ^{2} - 9}

Remove the parentheses

\frac{- 2 x ^{2} \times 6 x \times 8}{x ^{2} - 9}

Multiply

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Multiply the terms

- 2 x^{2} \times 6 x \times 8

Multiply the terms

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Evaluate

2 \times 6 \times 8

Multiply the terms

12 \times 8

Multiply the numbers

96

- 96 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 96 x^{2 + 1}

Add the numbers

- 96 x^{3}

\frac{- 96 x ^{3}}{x ^{2} - 9}

Solution

- \frac{96 x ^{3}}{x ^{2} - 9}

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Find the excluded values

x = 3, x = - 3

Evaluate

\frac{( - 2 x ^{2} \times 6 x \times 8 )}{x ^{2} - 9}

To find the excluded values,set the denominators equal to 0

x^{2} - 9 = 0

Move the constant to the right-hand side and change its sign

x^{2} = 0 + 9

Removing 0 doesn't change the value,so remove it from the expression

x^{2} = 9

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

x = \pm 9

Simplify the expression

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Evaluate

9

Write the number in exponential form with the base of 3

3^{2}

Reduce the index of the radical and exponent with 2

3

x = \pm 3

Separate the equation into 2 possible cases

x = 3 x = - 3

Solution

x = 3, x = - 3

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Find the roots

x = 0

Evaluate

\frac{( - 2 x ^{2} \times 6 x \times 8 )}{x ^{2} - 9}

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

\frac{( - 2 x ^{2} \times 6 x \times 8 )}{x ^{2} - 9} = 0

Find the domain

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Evaluate

x^{2} - 9 \neq = 0

Move the constant to the right side

x^{2} \neq = 9

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

x \neq = \pm 9

Simplify the expression

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Evaluate

9

Write the number in exponential form with the base of 3

3^{2}

Reduce the index of the radical and exponent with 2

3

x \neq = \pm 3

Separate the inequality into 2 possible cases

{x \neq = 3 x \neq = - 3

Find the intersection

x \in (- \infty, - 3) \cup (- 3, 3) \cup (3, + \infty)

\frac{( - 2 x ^{2} \times 6 x \times 8 )}{x ^{2} - 9} = 0, x \in (- \infty, - 3) \cup (- 3, 3) \cup (3, + \infty)

Calculate

\frac{( - 2 x ^{2} \times 6 x \times 8 )}{x ^{2} - 9} = 0

Multiply

More Steps

Multiply the terms

- 2 x^{2} \times 6 x \times 8

Multiply the terms

More Steps

Evaluate

2 \times 6 \times 8

Multiply the terms

12 \times 8

Multiply the numbers

96

- 96 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 96 x^{2 + 1}

Add the numbers

- 96 x^{3}

\frac{( - 96 x ^{3} )}{x ^{2} - 9} = 0

Remove the parentheses

\frac{- 96 x ^{3}}{x ^{2} - 9} = 0

Cross multiply

- 96 x^{3} = (x^{2} - 9) \times 0

Simplify the equation

- 96 x^{3} = 0

Change the signs on both sides of the equation

96 x^{3} = 0

Rewrite the expression

x^{3} = 0

The only way a power can be 0 is when the base equals 0

x = 0

Check if the solution is in the defined range

x = 0, x \in (- \infty, - 3) \cup (- 3, 3) \cup (3, + \infty)

Solution

x = 0

Show Solution