Algebra Examples

$f (x) = \frac{6}{x - 3}$ , $g (x) = \frac{4}{7 x}$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (\frac{6}{x - 3})$ by substituting in the value of $f$ into $g$ .

$g (\frac{6}{x - 3}) = \frac{4}{7 (\frac{6}{x - 3})}$

Step 3

Combine $7$ and $\frac{6}{x - 3}$ .

$g (\frac{6}{x - 3}) = \frac{4}{\frac{7 \cdot 6}{x - 3}}$

Step 4

Multiply $7$ by $6$ .

$g (\frac{6}{x - 3}) = \frac{4}{\frac{42}{x - 3}}$

Step 5

Multiply the numerator by the reciprocal of the denominator.

$g (\frac{6}{x - 3}) = 4 (\frac{x - 3}{42})$

Step 6

Cancel the common factor of $2$ .

Tap for more steps...

Step 6.1

Factor $2$ out of $4$ .

$g (\frac{6}{x - 3}) = 2 (2) (\frac{x - 3}{42})$

Step 6.2

Factor $2$ out of $42$ .

$g (\frac{6}{x - 3}) = 2 \cdot (2 (\frac{x - 3}{2 \cdot 21}))$

Step 6.3

Cancel the common factor.

$g (\frac{6}{x - 3}) = 2 \cdot (2 (\frac{x - 3}{2 \cdot 21}))$

Step 6.4

Rewrite the expression.

$g (\frac{6}{x - 3}) = 2 (\frac{x - 3}{21})$

Step 7

Combine $2$ and $\frac{x - 3}{21}$ .

$g (\frac{6}{x - 3}) = \frac{2 (x - 3)}{21}$