Precalculus Examples

$\frac{3 x + 6}{5 x^{2}} \cdot \frac{x}{x^{2 - 4}}$

Step 1

Factor $3$ out of $3 x + 6$ .

Tap for more steps...

Step 1.1

Factor $3$ out of $3 x$ .

$\frac{3 (x) + 6}{5 x^{2}} \cdot \frac{x}{x^{2 - 4}}$

Step 1.2

Factor $3$ out of $6$ .

$\frac{3 x + 3 \cdot 2}{5 x^{2}} \cdot \frac{x}{x^{2 - 4}}$

Step 1.3

Factor $3$ out of $3 x + 3 \cdot 2$ .

$\frac{3 (x + 2)}{5 x^{2}} \cdot \frac{x}{x^{2 - 4}}$

Step 2

Simplify the denominator.

Tap for more steps...

Step 2.1

Subtract $4$ from $2$ .

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

Step 2.2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{3 (x + 2)}{5 x^{2}} \cdot \frac{x}{\frac{1}{x^{2}}}$

Step 3

Simplify terms.

Tap for more steps...

Step 3.1

Combine.

$\frac{3 (x + 2) x}{5 x^{2} \frac{1}{x^{2}}}$

Step 3.2

Cancel the common factor of $x$ and $x^{2}$ .

Tap for more steps...

Step 3.2.1

Factor $x$ out of $3 (x + 2) x$ .

$\frac{x (3 (x + 2))}{5 x^{2} \frac{1}{x^{2}}}$

Step 3.2.2

Cancel the common factors.

Tap for more steps...

Step 3.2.2.1

Factor $x$ out of $5 x^{2} \frac{1}{x^{2}}$ .

$\frac{x (3 (x + 2))}{x (5 x \frac{1}{x^{2}})}$

Step 3.2.2.2

Cancel the common factor.

$\frac{x (3 (x + 2))}{x (5 x \frac{1}{x^{2}})}$

Step 3.2.2.3

Rewrite the expression.

$\frac{3 (x + 2)}{5 x \frac{1}{x^{2}}}$

Step 4

Simplify the denominator.

Tap for more steps...

Step 4.1

Combine $5$ and $\frac{1}{x^{2}}$ .

$\frac{3 (x + 2)}{x \frac{5}{x^{2}}}$

Step 4.2

Combine $x$ and $\frac{5}{x^{2}}$ .

$\frac{3 (x + 2)}{\frac{x \cdot 5}{x^{2}}}$

Step 5

Reduce the expression $\frac{x \cdot 5}{x^{2}}$ by cancelling the common factors.

Tap for more steps...

Step 5.1

Factor $x$ out of $x \cdot 5$ .

$\frac{3 (x + 2)}{\frac{x (5)}{x^{2}}}$

Step 5.2

Factor $x$ out of $x^{2}$ .

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

Step 5.3

Cancel the common factor.

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

Step 5.4

Rewrite the expression.

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

Step 6

Multiply the numerator by the reciprocal of the denominator.

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

Step 7

Apply the distributive property.

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

Step 8

Multiply $3$ by $2$ .

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

Step 9

Apply the distributive property.

$3 x \frac{x}{5} + 6 \frac{x}{5}$

Step 10

Multiply $3 x \frac{x}{5}$ .

Tap for more steps...

Step 10.1

Combine $3$ and $\frac{x}{5}$ .

$x \frac{3 x}{5} + 6 \frac{x}{5}$

Step 10.2

Combine $x$ and $\frac{3 x}{5}$ .

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

Step 10.3

Raise $x$ to the power of $1$ .

$\frac{3 (x^{1} x)}{5} + 6 \frac{x}{5}$

Step 10.4

Raise $x$ to the power of $1$ .

$\frac{3 (x^{1} x^{1})}{5} + 6 \frac{x}{5}$

Step 10.5

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

$\frac{3 x^{1 + 1}}{5} + 6 \frac{x}{5}$

Step 10.6

Add $1$ and $1$ .

$\frac{3 x^{2}}{5} + 6 \frac{x}{5}$

Step 11

Combine $6$ and $\frac{x}{5}$ .

$\frac{3 x^{2}}{5} + \frac{6 x}{5}$

Step 12

Combine the numerators over the common denominator.

$\frac{3 x^{2} + 6 x}{5}$

Step 13

Factor $3 x$ out of $3 x^{2} + 6 x$ .

Tap for more steps...

Step 13.1

Factor $3 x$ out of $3 x^{2}$ .

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

Step 13.2

Factor $3 x$ out of $6 x$ .

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

Step 13.3

Factor $3 x$ out of $3 x (x) + 3 x (2)$ .

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