Algebra Examples

$f (x) = \frac{1}{x - 4}$ , $g (x) = \frac{16}{x}$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (\frac{16}{x})$ by substituting in the value of $g$ into $f$ .

$f (\frac{16}{x}) = \frac{1}{(\frac{16}{x}) - 4}$

Step 3

Simplify the denominator.

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Step 3.1

Factor $4$ out of $\frac{16}{x} - 4$ .

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Step 3.1.1

Factor $4$ out of $\frac{16}{x}$ .

$f (\frac{16}{x}) = \frac{1}{4 (\frac{4}{x}) - 4}$

Step 3.1.2

Factor $4$ out of $- 4$ .

$f (\frac{16}{x}) = \frac{1}{4 (\frac{4}{x}) + 4 \cdot - 1}$

Step 3.1.3

Factor $4$ out of $4 \frac{4}{x} + 4 \cdot - 1$ .

$f (\frac{16}{x}) = \frac{1}{4 (\frac{4}{x} - 1)}$

Step 3.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$f (\frac{16}{x}) = \frac{1}{4 (\frac{4}{x} - 1 \cdot \frac{x}{x})}$

Step 3.3

Combine $- 1$ and $\frac{x}{x}$ .

$f (\frac{16}{x}) = \frac{1}{4 (\frac{4}{x} + \frac{- x}{x})}$

Step 3.4

Combine the numerators over the common denominator.

$f (\frac{16}{x}) = \frac{1}{4 (\frac{4 - x}{x})}$

Step 4

Combine $4$ and $\frac{4 - x}{x}$ .

$f (\frac{16}{x}) = \frac{1}{\frac{4 (4 - x)}{x}}$

Step 5

Multiply the numerator by the reciprocal of the denominator.

$f (\frac{16}{x}) = 1 (\frac{x}{4 (4 - x)})$

Step 6

Multiply $\frac{x}{4 (4 - x)}$ by $1$ .

$f (\frac{16}{x}) = \frac{x}{4 (4 - x)}$