Pre-Algebra Examples

$\frac{27 x^{4} - 8 x + 10}{9 x^{3}} - \frac{10 - 8 x}{9 x^{3}}$

Step 1

Combine the numerators over the common denominator.

$\frac{27 x^{4} - 8 x + 10 - (10 - 8 x)}{9 x^{3}}$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$\frac{27 x^{4} - 8 x + 10 - 1 \cdot 10 - (- 8 x)}{9 x^{3}}$

Step 2.2

Multiply $- 1$ by $10$ .

$\frac{27 x^{4} - 8 x + 10 - 10 - (- 8 x)}{9 x^{3}}$

Step 2.3

Multiply $- 8$ by $- 1$ .

$\frac{27 x^{4} - 8 x + 10 - 10 + 8 x}{9 x^{3}}$

Step 3

Simplify terms.

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Step 3.1

Combine the opposite terms in $27 x^{4} - 8 x + 10 - 10 + 8 x$ .

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Step 3.1.1

Subtract $10$ from $10$ .

$\frac{27 x^{4} - 8 x + 0 + 8 x}{9 x^{3}}$

Step 3.1.2

Add $27 x^{4} - 8 x$ and $0$ .

$\frac{27 x^{4} - 8 x + 8 x}{9 x^{3}}$

Step 3.1.3

Add $- 8 x$ and $8 x$ .

$\frac{27 x^{4} + 0}{9 x^{3}}$

Step 3.1.4

Add $27 x^{4}$ and $0$ .

$\frac{27 x^{4}}{9 x^{3}}$

Step 3.2

Cancel the common factor of $27$ and $9$ .

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Step 3.2.1

Factor $9$ out of $27 x^{4}$ .

$\frac{9 (3 x^{4})}{9 x^{3}}$

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Factor $9$ out of $9 x^{3}$ .

$\frac{9 (3 x^{4})}{9 (x^{3})}$

Step 3.2.2.2

Cancel the common factor.

$\frac{9 (3 x^{4})}{9 x^{3}}$

Step 3.2.2.3

Rewrite the expression.

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

Step 3.3

Cancel the common factor of $x^{4}$ and $x^{3}$ .

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Step 3.3.1

Factor $x^{3}$ out of $3 x^{4}$ .

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

Step 3.3.2

Cancel the common factors.

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Step 3.3.2.1

Multiply by $1$ .

$\frac{x^{3} (3 x)}{x^{3} \cdot 1}$

Step 3.3.2.2

Cancel the common factor.

$\frac{x^{3} (3 x)}{x^{3} \cdot 1}$

Step 3.3.2.3

Rewrite the expression.

$\frac{3 x}{1}$

Step 3.3.2.4

Divide $3 x$ by $1$ .

$3 x$