Algebra Examples

$f (x) = \frac{2}{x - 5}$ , $g (x) = \frac{2}{7 x}$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (\frac{2}{x - 5})$ by substituting in the value of $f$ into $g$ .

$g (\frac{2}{x - 5}) = \frac{2}{7 (\frac{2}{x - 5})}$

Step 3

Combine $7$ and $\frac{2}{x - 5}$ .

$g (\frac{2}{x - 5}) = \frac{2}{\frac{7 \cdot 2}{x - 5}}$

Step 4

Multiply $7$ by $2$ .

$g (\frac{2}{x - 5}) = \frac{2}{\frac{14}{x - 5}}$

Step 5

Multiply the numerator by the reciprocal of the denominator.

$g (\frac{2}{x - 5}) = 2 (\frac{x - 5}{14})$

Step 6

Cancel the common factor of $2$ .

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Step 6.1

Factor $2$ out of $14$ .

$g (\frac{2}{x - 5}) = 2 (\frac{x - 5}{2 (7)})$

Step 6.2

Cancel the common factor.

$g (\frac{2}{x - 5}) = 2 (\frac{x - 5}{2 \cdot 7})$

Step 6.3

Rewrite the expression.

$g (\frac{2}{x - 5}) = \frac{x - 5}{7}$