Solve (\frac{x 16}{x^2 2x-24})

Question

Simplify the expression

\frac{8 x}{x ^{3} - 12}

Evaluate

\frac{x \times 16}{x ^{2} \times 2 x - 24}

Multiply

More Steps

Multiply the terms

x^{2} \times 2 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 2

Add the numbers

x^{3} \times 2

Use the commutative property to reorder the terms

2 x^{3}

\frac{x \times 16}{2 x ^{3} - 24}

Use the commutative property to reorder the terms

\frac{16 x}{2 x ^{3} - 24}

Rewrite the fraction

\frac{16 x}{2 ( x ^{3} - 12 )}

Solution

\frac{8 x}{x ^{3} - 12}

Show Solution

Find the excluded values

x = 312

Evaluate

(\frac{x \times 16}{x ^{2} \times 2 x - 24})

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

x^{2} \times 2 x - 24 = 0

Multiply

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Evaluate

x^{2} \times 2 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 2

Add the numbers

x^{3} \times 2

Use the commutative property to reorder the terms

2 x^{3}

2 x^{3} - 24 = 0

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

2 x^{3} = 0 + 24

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

2 x^{3} = 24

Divide both sides

\frac{2 x ^{3}}{2} = \frac{24}{2}

Divide the numbers

x^{3} = \frac{24}{2}

Divide the numbers

More Steps

Evaluate

\frac{24}{2}

Reduce the numbers

\frac{12}{1}

Calculate

12

x^{3} = 12

Take the 3 -th root on both sides of the equation

3 x^{3} = 312

Solution

x = 312

Show Solution

Find the roots

x = 0

Evaluate

(\frac{x \times 16}{x ^{2} \times 2 x - 24})

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

\frac{x \times 16}{x ^{2} \times 2 x - 24} = 0

Find the domain

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Evaluate

x^{2} \times 2 x - 24 \neq = 0

Multiply

More Steps

Evaluate

x^{2} \times 2 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 2

Add the numbers

x^{3} \times 2

Use the commutative property to reorder the terms

2 x^{3}

2 x^{3} - 24 \neq = 0

Move the constant to the right side

2 x^{3} \neq = 24

Divide both sides

\frac{2 x ^{3}}{2} \neq = \frac{24}{2}

Divide the numbers

x^{3} \neq = \frac{24}{2}

Divide the numbers

More Steps

Evaluate

\frac{24}{2}

Reduce the numbers

\frac{12}{1}

Calculate

12

x^{3} \neq = 12

Take the 3 -th root on both sides of the equation

3 x^{3} \neq = 312

Calculate

x \neq = 312

\frac{x \times 16}{x ^{2} \times 2 x - 24} = 0, x \neq = 312

Calculate

\frac{x \times 16}{x ^{2} \times 2 x - 24} = 0

Multiply

More Steps

Multiply the terms

x^{2} \times 2 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 2

Add the numbers

x^{3} \times 2

Use the commutative property to reorder the terms

2 x^{3}

\frac{x \times 16}{2 x ^{3} - 24} = 0

Use the commutative property to reorder the terms

\frac{16 x}{2 x ^{3} - 24} = 0

Divide the terms

More Steps

Evaluate

\frac{16 x}{2 x ^{3} - 24}

Rewrite the fraction

\frac{16 x}{2 ( x ^{3} - 12 )}

Reduce the fraction

\frac{8 x}{x ^{3} - 12}

\frac{8 x}{x ^{3} - 12} = 0

Cross multiply

8 x = (x^{3} - 12) \times 0

Simplify the equation

8 x = 0

Rewrite the expression

x = 0

Check if the solution is in the defined range

x = 0, x \neq = 312

Solution

x = 0

Show Solution