Algebra Examples

$g (x) = 3 x - 5$ $h (x) = \frac{2}{2 x + 3}$

Step 1

Set up the composite result function.

$h (g (x))$

Step 2

Evaluate $h (3 x - 5)$ by substituting in the value of $g$ into $h$ .

$h (3 x - 5) = \frac{2}{2 (3 x - 5) + 3}$

Step 3

Simplify the denominator.

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Step 3.1

Apply the distributive property.

$h (3 x - 5) = \frac{2}{2 (3 x) + 2 \cdot - 5 + 3}$

Step 3.2

Multiply $3$ by $2$ .

$h (3 x - 5) = \frac{2}{6 x + 2 \cdot - 5 + 3}$

Step 3.3

Multiply $2$ by $- 5$ .

$h (3 x - 5) = \frac{2}{6 x - 10 + 3}$

Step 3.4

Add $- 10$ and $3$ .

$h (3 x - 5) = \frac{2}{6 x - 7}$