Simplify (9x+9)/(4x+8)*(2x+4)/(3x^2-3)

$\frac{9 x + 9}{4 x + 8} \cdot \frac{2 x + 4}{3 x^{2} - 3}$

Step 1

Simplify with factoring out.

Factor $9$ out of $9 x + 9$ .

Factor $9$ out of $9 x$ .

$\frac{9 (x) + 9}{4 x + 8} \cdot \frac{2 x + 4}{3 x^{2} - 3}$

Factor $9$ out of $9$ .

$\frac{9 (x) + 9 (1)}{4 x + 8} \cdot \frac{2 x + 4}{3 x^{2} - 3}$

Factor $9$ out of $9 (x) + 9 (1)$ .

$\frac{9 (x + 1)}{4 x + 8} \cdot \frac{2 x + 4}{3 x^{2} - 3}$

Factor $4$ out of $4 x + 8$ .

Factor $4$ out of $4 x$ .

$\frac{9 (x + 1)}{4 (x) + 8} \cdot \frac{2 x + 4}{3 x^{2} - 3}$

Factor $4$ out of $8$ .

$\frac{9 (x + 1)}{4 x + 4 \cdot 2} \cdot \frac{2 x + 4}{3 x^{2} - 3}$

Factor $4$ out of $4 x + 4 \cdot 2$ .

$\frac{9 (x + 1)}{4 (x + 2)} \cdot \frac{2 x + 4}{3 x^{2} - 3}$

Factor $2$ out of $2 x + 4$ .

Factor $2$ out of $2 x$ .

$\frac{9 (x + 1)}{4 (x + 2)} \cdot \frac{2 (x) + 4}{3 x^{2} - 3}$

Factor $2$ out of $4$ .

$\frac{9 (x + 1)}{4 (x + 2)} \cdot \frac{2 x + 2 \cdot 2}{3 x^{2} - 3}$

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

$\frac{9 (x + 1)}{4 (x + 2)} \cdot \frac{2 (x + 2)}{3 x^{2} - 3}$

Step 2

Simplify the denominator.

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

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

$\frac{9 (x + 1)}{4 (x + 2)} \cdot \frac{2 (x + 2)}{3 (x^{2}) - 3}$

Factor $3$ out of $- 3$ .

$\frac{9 (x + 1)}{4 (x + 2)} \cdot \frac{2 (x + 2)}{3 (x^{2}) + 3 (- 1)}$

Factor $3$ out of $3 (x^{2}) + 3 (- 1)$ .

$\frac{9 (x + 1)}{4 (x + 2)} \cdot \frac{2 (x + 2)}{3 (x^{2} - 1)}$

Rewrite $1$ as $1^{2}$ .

$\frac{9 (x + 1)}{4 (x + 2)} \cdot \frac{2 (x + 2)}{3 (x^{2} - 1^{2})}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 1$ .

$\frac{9 (x + 1)}{4 (x + 2)} \cdot \frac{2 (x + 2)}{3 (x + 1) (x - 1)}$

Step 3

Simplify terms.

Cancel the common factor of $3 (x + 1)$ .

Factor $3 (x + 1)$ out of $9 (x + 1)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $2 (x + 2)$ .

Factor $2 (x + 2)$ out of $4 (x + 2)$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{3}{2} \cdot \frac{1}{x - 1}$

Multiply $\frac{3}{2}$ by $\frac{1}{x - 1}$ .

$\frac{3}{2 (x - 1)}$

Simplify (9x+9)/(4x+8)*(2x+4)/(3x^2-3)

Related Questions

Support LCMGCF.com by disabling your adblocker.