Pre-Algebra Examples

$x + \frac{8}{x^{2}} \div x - \frac{16}{x^{3}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite the division as a fraction.

$x + \frac{\frac{8}{x^{2}}}{x} - \frac{16}{x^{3}}$

Step 1.2

Multiply the numerator by the reciprocal of the denominator.

$x + \frac{8}{x^{2}} \cdot \frac{1}{x} - \frac{16}{x^{3}}$

Step 1.3

Combine.

$x + \frac{8 \cdot 1}{x^{2} x} - \frac{16}{x^{3}}$

Step 1.4

Multiply $x^{2}$ by $x$ by adding the exponents.

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Step 1.4.1

Multiply $x^{2}$ by $x$ .

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Step 1.4.1.1

Raise $x$ to the power of $1$ .

$x + \frac{8 \cdot 1}{x^{2} x^{1}} - \frac{16}{x^{3}}$

Step 1.4.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x + \frac{8 \cdot 1}{x^{2 + 1}} - \frac{16}{x^{3}}$

Step 1.4.2

Add $2$ and $1$ .

$x + \frac{8 \cdot 1}{x^{3}} - \frac{16}{x^{3}}$

Step 1.5

Multiply $8$ by $1$ .

$x + \frac{8}{x^{3}} - \frac{16}{x^{3}}$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

$x + \frac{8 - 16}{x^{3}}$

Step 2.2

Simplify the expression.

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Step 2.2.1

Subtract $16$ from $8$ .

$x + \frac{- 8}{x^{3}}$

Step 2.2.2

Move the negative in front of the fraction.

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

Step 3

To write $x$ as a fraction with a common denominator, multiply by $\frac{x^{3}}{x^{3}}$ .

$\frac{x \cdot x^{3}}{x^{3}} - \frac{8}{x^{3}}$

Step 4

Combine the numerators over the common denominator.

$\frac{x \cdot x^{3} - 8}{x^{3}}$

Step 5

Multiply $x$ by $x^{3}$ by adding the exponents.

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Step 5.1

Multiply $x$ by $x^{3}$ .

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Step 5.1.1

Raise $x$ to the power of $1$ .

$\frac{x^{1} x^{3} - 8}{x^{3}}$

Step 5.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{x^{1 + 3} - 8}{x^{3}}$

Step 5.2

Add $1$ and $3$ .

$\frac{x^{4} - 8}{x^{3}}$