Calculus Examples

$\frac{x^{2} - 4 x}{\sqrt{x}}$

Step 1

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

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Step 1.1

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

$\frac{x \cdot x - 4 x}{\sqrt{x}}$

Step 1.2

Factor $x$ out of $- 4 x$ .

$\frac{x \cdot x + x \cdot - 4}{\sqrt{x}}$

Step 1.3

Factor $x$ out of $x \cdot x + x \cdot - 4$ .

$\frac{x (x - 4)}{\sqrt{x}}$

Step 2

Multiply $\frac{x (x - 4)}{\sqrt{x}}$ by $\frac{\sqrt{x}}{\sqrt{x}}$ .

$\frac{x (x - 4)}{\sqrt{x}} \cdot \frac{\sqrt{x}}{\sqrt{x}}$

Step 3

Combine and simplify the denominator.

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Step 3.1

Multiply $\frac{x (x - 4)}{\sqrt{x}}$ by $\frac{\sqrt{x}}{\sqrt{x}}$ .

$\frac{x (x - 4) \sqrt{x}}{\sqrt{x} \sqrt{x}}$

Step 3.2

Raise $\sqrt{x}$ to the power of $1$ .

$\frac{x (x - 4) \sqrt{x}}{{\sqrt{x}}^{1} \sqrt{x}}$

Step 3.3

Raise $\sqrt{x}$ to the power of $1$ .

$\frac{x (x - 4) \sqrt{x}}{{\sqrt{x}}^{1} {\sqrt{x}}^{1}}$

Step 3.4

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

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

Step 3.5

Add $1$ and $1$ .

$\frac{x (x - 4) \sqrt{x}}{{\sqrt{x}}^{2}}$

Step 3.6

Rewrite ${\sqrt{x}}^{2}$ as $x$ .

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Step 3.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x}$ as $x^{\frac{1}{2}}$ .

$\frac{x (x - 4) \sqrt{x}}{{(x^{\frac{1}{2}})}^{2}}$

Step 3.6.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{x (x - 4) \sqrt{x}}{x^{\frac{1}{2} \cdot 2}}$

Step 3.6.3

Combine $\frac{1}{2}$ and $2$ .

$\frac{x (x - 4) \sqrt{x}}{x^{\frac{2}{2}}}$

Step 3.6.4

Cancel the common factor of $2$ .

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Step 3.6.4.1

Cancel the common factor.

$\frac{x (x - 4) \sqrt{x}}{x^{\frac{2}{2}}}$

Step 3.6.4.2

Rewrite the expression.

$\frac{x (x - 4) \sqrt{x}}{x^{1}}$

Step 3.6.5

Simplify.

$\frac{x (x - 4) \sqrt{x}}{x}$

Step 4

Cancel the common factor of $x$ .

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Step 4.1

Cancel the common factor.

$\frac{x (x - 4) \sqrt{x}}{x}$

Step 4.2

Divide $(x - 4) \sqrt{x}$ by $1$ .

$(x - 4) \sqrt{x}$

Step 5

Apply the distributive property.

$x \sqrt{x} - 4 \sqrt{x}$