Algebra Examples

$(36 x^{3} + 9 x^{2} + 45 x) \div 9 x^{2}$

Step 1

Rewrite the division as a fraction.

$\frac{36 x^{3} + 9 x^{2} + 45 x}{9 x^{2}}$

Step 2

Factor $9 x$ out of $36 x^{3} + 9 x^{2} + 45 x$ .

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Step 2.1

Factor $9 x$ out of $36 x^{3}$ .

$\frac{9 x (4 x^{2}) + 9 x^{2} + 45 x}{9 x^{2}}$

Step 2.2

Factor $9 x$ out of $9 x^{2}$ .

$\frac{9 x (4 x^{2}) + 9 x (x) + 45 x}{9 x^{2}}$

Step 2.3

Factor $9 x$ out of $45 x$ .

$\frac{9 x (4 x^{2}) + 9 x (x) + 9 x (5)}{9 x^{2}}$

Step 2.4

Factor $9 x$ out of $9 x (4 x^{2}) + 9 x (x)$ .

$\frac{9 x (4 x^{2} + x) + 9 x (5)}{9 x^{2}}$

Step 2.5

Factor $9 x$ out of $9 x (4 x^{2} + x) + 9 x (5)$ .

$\frac{9 x (4 x^{2} + x + 5)}{9 x^{2}}$

Step 3

Cancel the common factor of $9$ .

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Step 3.1

Cancel the common factor.

$\frac{9 x (4 x^{2} + x + 5)}{9 x^{2}}$

Step 3.2

Rewrite the expression.

$\frac{x (4 x^{2} + x + 5)}{x^{2}}$

Step 4

Cancel the common factors.

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Step 4.1

Factor $x$ out of $x^{2}$ .

$\frac{x (4 x^{2} + x + 5)}{x \cdot x}$

Step 4.2

Cancel the common factor.

$\frac{x (4 x^{2} + x + 5)}{x \cdot x}$

Step 4.3

Rewrite the expression.

$\frac{4 x^{2} + x + 5}{x}$

Step 5

Split the fraction $\frac{4 x^{2} + x + 5}{x}$ into two fractions.

$\frac{4 x^{2} + x}{x} + \frac{5}{x}$

Step 6

Split the fraction $\frac{4 x^{2} + x}{x}$ into two fractions.

$\frac{4 x^{2}}{x} + \frac{x}{x} + \frac{5}{x}$

Step 7

Cancel the common factor of $x^{2}$ and $x$ .

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Step 7.1

Factor $x$ out of $4 x^{2}$ .

$\frac{x (4 x)}{x} + \frac{x}{x} + \frac{5}{x}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

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

$\frac{x (4 x)}{x^{1}} + \frac{x}{x} + \frac{5}{x}$

Step 7.2.2

Factor $x$ out of $x^{1}$ .

$\frac{x (4 x)}{x \cdot 1} + \frac{x}{x} + \frac{5}{x}$

Step 7.2.3

Cancel the common factor.

$\frac{x (4 x)}{x \cdot 1} + \frac{x}{x} + \frac{5}{x}$

Step 7.2.4

Rewrite the expression.

$\frac{4 x}{1} + \frac{x}{x} + \frac{5}{x}$

Step 7.2.5

Divide $4 x$ by $1$ .

$4 x + \frac{x}{x} + \frac{5}{x}$

Step 8

Cancel the common factor of $x$ .

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Step 8.1

Cancel the common factor.

$4 x + \frac{x}{x} + \frac{5}{x}$

Step 8.2

Rewrite the expression.

$4 x + 1 + \frac{5}{x}$