Algebra Examples

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

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (\frac{4}{7 x})$ by substituting in the value of $g$ into $f$ .

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

Step 3

Simplify the denominator.

Tap for more steps...

Step 3.1

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{7 x}{7 x}$ .

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

Step 3.2

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

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

Step 3.3

Combine the numerators over the common denominator.

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

Step 3.4

Multiply $- 3$ by $7$ .

$f (\frac{4}{7 x}) = \frac{6}{\frac{4 - 21 x}{7 x}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$f (\frac{4}{7 x}) = 6 (\frac{7 x}{4 - 21 x})$

Step 5

Multiply $6 \frac{7 x}{4 - 21 x}$ .

Tap for more steps...

Step 5.1

Combine $6$ and $\frac{7 x}{4 - 21 x}$ .

$f (\frac{4}{7 x}) = \frac{6 (7 x)}{4 - 21 x}$

Step 5.2

Multiply $7$ by $6$ .

$f (\frac{4}{7 x}) = \frac{42 x}{4 - 21 x}$