Finite Math Examples

$x^{4} - 6 x^{2} - 29 \div x + 3$

Step 1

Rewrite the division as a fraction.

$x^{4} - 6 x^{2} - \frac{29}{x} + 3$

Step 2

To write $x^{4}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$- 6 x^{2} + \frac{x^{4} x}{x} - \frac{29}{x} + 3$

Step 3

Combine the numerators over the common denominator.

$- 6 x^{2} + \frac{x^{4} x - 29}{x} + 3$

Step 4

Multiply $x^{4}$ by $x$ by adding the exponents.

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Step 4.1

Multiply $x^{4}$ by $x$ .

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Step 4.1.1

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

$- 6 x^{2} + \frac{x^{4} x^{1} - 29}{x} + 3$

Step 4.1.2

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

$- 6 x^{2} + \frac{x^{4 + 1} - 29}{x} + 3$

Step 4.2

Add $4$ and $1$ .

$- 6 x^{2} + \frac{x^{5} - 29}{x} + 3$

Step 5

To write $- 6 x^{2}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$- 6 x^{2} \cdot \frac{x}{x} + \frac{x^{5} - 29}{x} + 3$

Step 6

Simplify terms.

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Step 6.1

Combine $- 6 x^{2}$ and $\frac{x}{x}$ .

$\frac{- 6 x^{2} x}{x} + \frac{x^{5} - 29}{x} + 3$

Step 6.2

Combine the numerators over the common denominator.

$\frac{- 6 x^{2} x + x^{5} - 29}{x} + 3$

Step 7

Simplify the numerator.

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Step 7.1

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

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Step 7.1.1

Move $x$ .

$\frac{- 6 (x \cdot x^{2}) + x^{5} - 29}{x} + 3$

Step 7.1.2

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

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Step 7.1.2.1

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

$\frac{- 6 (x^{1} x^{2}) + x^{5} - 29}{x} + 3$

Step 7.1.2.2

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

$\frac{- 6 x^{1 + 2} + x^{5} - 29}{x} + 3$

Step 7.1.3

Add $1$ and $2$ .

$\frac{- 6 x^{3} + x^{5} - 29}{x} + 3$

Step 7.2

Reorder terms.

$\frac{x^{5} - 6 x^{3} - 29}{x} + 3$

Step 8

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

$\frac{x^{5} - 6 x^{3} - 29}{x} + \frac{3 x}{x}$

Step 9

Combine the numerators over the common denominator.

$\frac{x^{5} - 6 x^{3} - 29 + 3 x}{x}$

Step 10

Reorder terms.

$\frac{x^{5} - 6 x^{3} + 3 x - 29}{x}$