Algebra Examples

$f (x) = \frac{8}{x + 8}$ , $g (x) = \frac{6}{5 x}$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (\frac{6}{5 x})$ by substituting in the value of $g$ into $f$ .

$f (\frac{6}{5 x}) = \frac{8}{(\frac{6}{5 x}) + 8}$

Step 3

Cancel the common factor of $8$ and $(\frac{6}{5 x}) + 8$ .

Tap for more steps...

Step 3.1

Factor $2$ out of $8$ .

$f (\frac{6}{5 x}) = \frac{2 (4)}{(\frac{6}{5 x}) + 8}$

Step 3.2

Cancel the common factors.

Tap for more steps...

Step 3.2.1

Factor $2$ out of $\frac{6}{5 x}$ .

$f (\frac{6}{5 x}) = \frac{2 \cdot 4}{2 (\frac{3}{5 x}) + 8}$

Step 3.2.2

Factor $2$ out of $8$ .

$f (\frac{6}{5 x}) = \frac{2 (4)}{2 (\frac{3}{5 x}) + 2 \cdot 4}$

Step 3.2.3

Factor $2$ out of $2 \frac{3}{5 x} + 2 \cdot 4$ .

$f (\frac{6}{5 x}) = \frac{2 (4)}{2 (\frac{3}{5 x} + 4)}$

Step 3.2.4

Cancel the common factor.

$f (\frac{6}{5 x}) = \frac{2 \cdot 4}{2 (\frac{3}{5 x} + 4)}$

Step 3.2.5

Rewrite the expression.

$f (\frac{6}{5 x}) = \frac{4}{\frac{3}{5 x} + 4}$

Step 4

Simplify the denominator.

Tap for more steps...

Step 4.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{5 x}{5 x}$ .

$f (\frac{6}{5 x}) = \frac{4}{\frac{3}{5 x} + 4 \cdot \frac{5 x}{5 x}}$

Step 4.2

Combine $4$ and $\frac{5 x}{5 x}$ .

$f (\frac{6}{5 x}) = \frac{4}{\frac{3}{5 x} + \frac{4 (5 x)}{5 x}}$

Step 4.3

Combine the numerators over the common denominator.

$f (\frac{6}{5 x}) = \frac{4}{\frac{3 + 4 (5 x)}{5 x}}$

Step 4.4

Multiply $4$ by $5$ .

$f (\frac{6}{5 x}) = \frac{4}{\frac{3 + 20 x}{5 x}}$

Step 5

Multiply the numerator by the reciprocal of the denominator.

$f (\frac{6}{5 x}) = 4 (\frac{5 x}{3 + 20 x})$

Step 6

Multiply $4 \frac{5 x}{3 + 20 x}$ .

Tap for more steps...

Step 6.1

Combine $4$ and $\frac{5 x}{3 + 20 x}$ .

$f (\frac{6}{5 x}) = \frac{4 (5 x)}{3 + 20 x}$

Step 6.2

Multiply $5$ by $4$ .

$f (\frac{6}{5 x}) = \frac{20 x}{3 + 20 x}$