Precalculus Examples

$f (x) = \frac{x}{x + 2}$ , $g (x) = \frac{2}{x}$ , $(f \cdot f) \cdot (x)$

Step 1

Replace the function designators in $(f \cdot f) \cdot (x)$ with the actual functions.

$((\frac{x}{x + 2}) \cdot (\frac{x}{x + 2})) \cdot (x)$

Step 2

Simplify $((\frac{x}{x + 2}) \cdot (\frac{x}{x + 2})) \cdot (x)$ .

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Step 2.1

Multiply $(\frac{x}{x + 2}) (\frac{x}{x + 2})$ .

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Step 2.1.1

Multiply $\frac{x}{x + 2}$ by $\frac{x}{x + 2}$ .

$\frac{x \cdot x}{(x + 2) (x + 2)} \cdot x$

Step 2.1.2

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

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

Step 2.1.3

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

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

Step 2.1.4

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

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

Step 2.1.5

Add $1$ and $1$ .

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

Step 2.1.6

Raise $x + 2$ to the power of $1$ .

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

Step 2.1.7

Raise $x + 2$ to the power of $1$ .

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

Step 2.1.8

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

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

Step 2.1.9

Add $1$ and $1$ .

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

Step 2.2

Multiply $\frac{x^{2}}{{(x + 2)}^{2}} x$ .

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Step 2.2.1

Combine $\frac{x^{2}}{{(x + 2)}^{2}}$ and $x$ .

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

Step 2.2.2

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

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Step 2.2.2.1

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

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Step 2.2.2.1.1

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

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

Step 2.2.2.1.2

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

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

Step 2.2.2.2

Add $2$ and $1$ .

$\frac{x^{3}}{{(x + 2)}^{2}}$