Algebra Examples

$\frac{x + 3}{4 x} \cdot \frac{3 x - 18}{6 x + 18} \cdot \frac{x^{2}}{4 x + 12}$

Step 1

Factor $4$ out of $4 x + 12$ .

Tap for more steps...

Step 1.1

Factor $4$ out of $4 x$ .

$\frac{x + 3}{4 x} \cdot \frac{3 x - 18}{6 x + 18} \cdot \frac{x^{2}}{4 (x) + 12}$

Step 1.2

Factor $4$ out of $12$ .

$\frac{x + 3}{4 x} \cdot \frac{3 x - 18}{6 x + 18} \cdot \frac{x^{2}}{4 x + 4 \cdot 3}$

Step 1.3

Factor $4$ out of $4 x + 4 \cdot 3$ .

$\frac{x + 3}{4 x} \cdot \frac{3 x - 18}{6 x + 18} \cdot \frac{x^{2}}{4 (x + 3)}$

Step 2

Factor $3$ out of $3 x - 18$ .

Tap for more steps...

Step 2.1

Factor $3$ out of $3 x$ .

$\frac{x + 3}{4 x} \cdot \frac{3 (x) - 18}{6 x + 18} \cdot \frac{x^{2}}{4 (x + 3)}$

Step 2.2

Factor $3$ out of $- 18$ .

$\frac{x + 3}{4 x} \cdot \frac{3 x + 3 \cdot - 6}{6 x + 18} \cdot \frac{x^{2}}{4 (x + 3)}$

Step 2.3

Factor $3$ out of $3 x + 3 \cdot - 6$ .

$\frac{x + 3}{4 x} \cdot \frac{3 (x - 6)}{6 x + 18} \cdot \frac{x^{2}}{4 (x + 3)}$

Step 3

Factor $6$ out of $6 x + 18$ .

Tap for more steps...

Step 3.1

Factor $6$ out of $6 x$ .

$\frac{x + 3}{4 x} \cdot \frac{3 (x - 6)}{6 (x) + 18} \cdot \frac{x^{2}}{4 (x + 3)}$

Step 3.2

Factor $6$ out of $18$ .

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

Step 3.3

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

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

Step 4

Cancel the common factor of $x + 3$ .

Tap for more steps...

Step 4.1

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

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

Step 4.2

Cancel the common factor.

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

Step 4.3

Rewrite the expression.

$\frac{1}{4 x} \cdot \frac{3 (x - 6)}{6} \cdot \frac{x^{2}}{4 (x + 3)}$

Step 5

Multiply $\frac{1}{4 x}$ by $\frac{3 (x - 6)}{6}$ .

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

Step 6

Multiply $6$ by $4$ .

$\frac{3 (x - 6)}{24 x} \cdot \frac{x^{2}}{4 (x + 3)}$

Step 7

Combine.

$\frac{3 (x - 6) x^{2}}{24 x (4 (x + 3))}$

Step 8

Cancel the common factor of $3$ and $24$ .

Tap for more steps...

Step 8.1

Factor $3$ out of $3 (x - 6) x^{2}$ .

$\frac{3 ((x - 6) x^{2})}{24 x (4 (x + 3))}$

Step 8.2

Cancel the common factors.

Tap for more steps...

Step 8.2.1

Factor $3$ out of $24 x (4 (x + 3))$ .

$\frac{3 ((x - 6) x^{2})}{3 (8 x (4 (x + 3)))}$

Step 8.2.2

Cancel the common factor.

$\frac{3 ((x - 6) x^{2})}{3 (8 x (4 (x + 3)))}$

Step 8.2.3

Rewrite the expression.

$\frac{(x - 6) x^{2}}{8 x (4 (x + 3))}$

Step 9

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

Tap for more steps...

Step 9.1

Factor $x$ out of $(x - 6) x^{2}$ .

$\frac{x ((x - 6) x)}{8 x (4 (x + 3))}$

Step 9.2

Cancel the common factors.

Tap for more steps...

Step 9.2.1

Factor $x$ out of $8 x (4 (x + 3))$ .

$\frac{x ((x - 6) x)}{x (8 (4 (x + 3)))}$

Step 9.2.2

Cancel the common factor.

$\frac{x ((x - 6) x)}{x (8 (4 (x + 3)))}$

Step 9.2.3

Rewrite the expression.

$\frac{(x - 6) x}{8 (4 (x + 3))}$

Step 10

Simplify the expression.

Tap for more steps...

Step 10.1

Multiply $8$ by $4$ .

$\frac{(x - 6) x}{32 (x + 3)}$

Step 10.2

Reorder factors in $\frac{(x - 6) x}{32 (x + 3)}$ .

$\frac{x (x - 6)}{32 (x + 3)}$