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

Question

Simplify the expression

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

Evaluate

(\frac{3}{x - 3}) (\frac{x}{x ^{3}})

Remove the unnecessary parentheses

\frac{3}{x - 3} \times (\frac{x}{x ^{3}})

Divide the terms

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Evaluate

\frac{x}{x ^{3}}

Use the product rule \frac{a ^{n}}{a ^{m}} = a^{n - m} to simplify the expression

\frac{1}{x ^{3 - 1}}

Reduce the fraction

\frac{1}{x ^{2}}

\frac{3}{x - 3} \times \frac{1}{x ^{2}}

Multiply the terms

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

Multiply the terms

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

Solution

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Evaluate

x^{2} (x - 3)

Apply the distributive property

x^{2} \times x - x^{2} \times 3

Multiply the terms

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Evaluate

x^{2} \times x

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{2 + 1}

Add the numbers

x^{3}

x^{3} - x^{2} \times 3

Use the commutative property to reorder the terms

x^{3} - 3 x^{2}

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

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Find the excluded values

x = 3, x = 0

Evaluate

(\frac{3}{x - 3}) (\frac{x}{x ^{3}})

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

x - 3 = 0 x^{3} = 0

Solve the equations

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Evaluate

x - 3 = 0

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

x = 0 + 3

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

x = 3

x = 3 x^{3} = 0

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

x = 3 x = 0

Solution

x = 3, x = 0

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Find the roots

x \in \emptyset

Evaluate

(\frac{3}{x - 3}) (\frac{x}{x ^{3}})

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

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

Find the domain

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Evaluate

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

Calculate

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Evaluate

x - 3 \neq = 0

Move the constant to the right side

x \neq = 0 + 3

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

x \neq = 3

{x \neq = 3 x^{3} \neq = 0

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

{x \neq = 3 x \neq = 0

Find the intersection

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

(\frac{3}{x - 3}) (\frac{x}{x ^{3}}) = 0, x \in (- \infty, 0) \cup (0, 3) \cup (3, + \infty)

Calculate

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

Remove the unnecessary parentheses

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

Divide the terms

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Evaluate

\frac{x}{x ^{3}}

Use the product rule \frac{a ^{n}}{a ^{m}} = a^{n - m} to simplify the expression

\frac{1}{x ^{3 - 1}}

Reduce the fraction

\frac{1}{x ^{2}}

\frac{3}{x - 3} \times \frac{1}{x ^{2}} = 0

Multiply the terms

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Multiply the terms

\frac{3}{x - 3} \times \frac{1}{x ^{2}}

Multiply the terms

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

Multiply the terms

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

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

Cross multiply

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

Simplify the equation

3 = 0

Solution

x \in \emptyset

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