Calculus Examples

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

Step 1

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

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Step 1.1

Factor $x^{4}$ out of $x^{5}$ .

$\frac{x^{4} x + 9 x^{4}}{x^{2}}$

Step 1.2

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

$\frac{x^{4} x + x^{4} \cdot 9}{x^{2}}$

Step 1.3

Factor $x^{4}$ out of $x^{4} x + x^{4} \cdot 9$ .

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

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

Step 2

Cancel the common factor of $x^{4}$ and $x^{2}$ .

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Step 2.1

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

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

Multiply by $1$ .

$\frac{x^{2} (x^{2} (x + 9))}{x^{2} \cdot 1}$

Step 2.2.2

Cancel the common factor.

$\frac{x^{2} (x^{2} (x + 9))}{x^{2} \cdot 1}$

Step 2.2.3

Rewrite the expression.

$\frac{x^{2} (x + 9)}{1}$

Step 2.2.4

Divide $x^{2} (x + 9)$ by $1$ .

$x^{2} (x + 9)$

$x^{2} (x + 9)$

$x^{2} (x + 9)$

Step 3

Apply the distributive property.

$x^{2} x + x^{2} \cdot 9$

Step 4

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

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Step 4.1

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

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Step 4.1.1

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

$x^{2} x^{1} + x^{2} \cdot 9$

Step 4.1.2

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

$x^{2 + 1} + x^{2} \cdot 9$

$x^{2 + 1} + x^{2} \cdot 9$

Step 4.2

Add $2$ and $1$ .

$x^{3} + x^{2} \cdot 9$

$x^{3} + x^{2} \cdot 9$

Step 5

Move $9$ to the left of $x^{2}$ .

$x^{3} + 9 x^{2}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$