Precalculus Examples

$f (x) = \frac{2 x + 9}{9 x - 2}$ , $g (x) = \frac{4 x}{9 x - 2}$ , $(f \cdot g) (x)$

Step 1

Evaluate $f \cdot g$ .

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Step 1.1

Replace the function designators in $f \cdot g$ with the actual functions.

$(\frac{2 x + 9}{9 x - 2}) \cdot (\frac{4 x}{9 x - 2})$

Step 1.2

Multiply $(\frac{2 x + 9}{9 x - 2}) (\frac{4 x}{9 x - 2})$ .

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Step 1.2.1

Multiply $\frac{2 x + 9}{9 x - 2}$ by $\frac{4 x}{9 x - 2}$ .

$\frac{(2 x + 9) (4 x)}{(9 x - 2) (9 x - 2)}$

Step 1.2.2

Raise $9 x - 2$ to the power of $1$ .

$\frac{(2 x + 9) (4 x)}{{(9 x - 2)}^{1} (9 x - 2)}$

Step 1.2.3

Raise $9 x - 2$ to the power of $1$ .

$\frac{(2 x + 9) (4 x)}{{(9 x - 2)}^{1} {(9 x - 2)}^{1}}$

Step 1.2.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{(2 x + 9) (4 x)}{{(9 x - 2)}^{1 + 1}}$

Step 1.2.5

Add $1$ and $1$ .

$\frac{(2 x + 9) (4 x)}{{(9 x - 2)}^{2}}$

Step 1.3

Move $4$ to the left of $2 x + 9$ .

$\frac{4 \cdot (2 x + 9) x}{{(9 x - 2)}^{2}}$

Step 1.4

Reorder factors in $\frac{4 (2 x + 9) x}{{(9 x - 2)}^{2}}$ .

$\frac{4 x (2 x + 9)}{{(9 x - 2)}^{2}}$

Step 2

Evaluate $f \cdot g$ at $x$ .

$\frac{4 (x) (2 (x) + 9)}{{(9 (x) - 2)}^{2}}$

Step 3

Simplify $\frac{4 (x) (2 (x) + 9)}{{(9 (x) - 2)}^{2}}$ .

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Step 3.1

Remove parentheses.

$\frac{4 (x) (2 (x) + 9)}{{(9 (x) - 2)}^{2}}$

Step 3.2

Multiply $9$ by $x$ .

$\frac{4 x (2 x + 9)}{{(9 x - 2)}^{2}}$