Algebra Examples

$f (x) = \frac{x}{x + 9}$ ; $g (x) = \frac{27}{x + 1}$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (\frac{x}{x + 9})$ by substituting in the value of $f$ into $g$ .

$g (\frac{x}{x + 9}) = \frac{27}{(\frac{x}{x + 9}) + 1}$

Step 3

Simplify the denominator.

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Step 3.1

Write $1$ as a fraction with a common denominator.

$g (\frac{x}{x + 9}) = \frac{27}{\frac{x}{x + 9} + \frac{x + 9}{x + 9}}$

Step 3.2

Combine the numerators over the common denominator.

$g (\frac{x}{x + 9}) = \frac{27}{\frac{x + x + 9}{x + 9}}$

Step 3.3

Add $x$ and $x$ .

$g (\frac{x}{x + 9}) = \frac{27}{\frac{2 x + 9}{x + 9}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$g (\frac{x}{x + 9}) = 27 (\frac{x + 9}{2 x + 9})$

Step 5

Combine $27$ and $\frac{x + 9}{2 x + 9}$ .

$g (\frac{x}{x + 9}) = \frac{27 (x + 9)}{2 x + 9}$