Simplify (24x+24)/(12x-4)*(48x-16)/(6x^2-6)

$\frac{24 x + 24}{12 x - 4} \cdot \frac{48 x - 16}{6 x^{2} - 6}$

Step 1

Simplify with factoring out.

Factor $24$ out of $24 x + 24$ .

Factor $24$ out of $24 x$ .

$\frac{24 (x) + 24}{12 x - 4} \cdot \frac{48 x - 16}{6 x^{2} - 6}$

Factor $24$ out of $24$ .

$\frac{24 (x) + 24 (1)}{12 x - 4} \cdot \frac{48 x - 16}{6 x^{2} - 6}$

Factor $24$ out of $24 (x) + 24 (1)$ .

$\frac{24 (x + 1)}{12 x - 4} \cdot \frac{48 x - 16}{6 x^{2} - 6}$

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

Factor $4$ out of $12 x$ .

$\frac{24 (x + 1)}{4 (3 x) - 4} \cdot \frac{48 x - 16}{6 x^{2} - 6}$

Factor $4$ out of $- 4$ .

$\frac{24 (x + 1)}{4 (3 x) + 4 (- 1)} \cdot \frac{48 x - 16}{6 x^{2} - 6}$

Factor $4$ out of $4 (3 x) + 4 (- 1)$ .

$\frac{24 (x + 1)}{4 (3 x - 1)} \cdot \frac{48 x - 16}{6 x^{2} - 6}$

Factor $16$ out of $48 x - 16$ .

Factor $16$ out of $48 x$ .

$\frac{24 (x + 1)}{4 (3 x - 1)} \cdot \frac{16 (3 x) - 16}{6 x^{2} - 6}$

Factor $16$ out of $- 16$ .

$\frac{24 (x + 1)}{4 (3 x - 1)} \cdot \frac{16 (3 x) + 16 (- 1)}{6 x^{2} - 6}$

Factor $16$ out of $16 (3 x) + 16 (- 1)$ .

$\frac{24 (x + 1)}{4 (3 x - 1)} \cdot \frac{16 (3 x - 1)}{6 x^{2} - 6}$

Step 2

Simplify the denominator.

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

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

$\frac{24 (x + 1)}{4 (3 x - 1)} \cdot \frac{16 (3 x - 1)}{6 (x^{2}) - 6}$

Factor $6$ out of $- 6$ .

$\frac{24 (x + 1)}{4 (3 x - 1)} \cdot \frac{16 (3 x - 1)}{6 (x^{2}) + 6 (- 1)}$

Factor $6$ out of $6 (x^{2}) + 6 (- 1)$ .

$\frac{24 (x + 1)}{4 (3 x - 1)} \cdot \frac{16 (3 x - 1)}{6 (x^{2} - 1)}$

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

$\frac{24 (x + 1)}{4 (3 x - 1)} \cdot \frac{16 (3 x - 1)}{6 (x^{2} - 1^{2})}$

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 $b = 1$ .

$\frac{24 (x + 1)}{4 (3 x - 1)} \cdot \frac{16 (3 x - 1)}{6 (x + 1) (x - 1)}$

Step 3

Simplify terms.

Cancel the common factor of $6 (x + 1)$ .

Factor $6 (x + 1)$ out of $24 (x + 1)$ .

$\frac{6 (x + 1) (4)}{4 (3 x - 1)} \cdot \frac{16 (3 x - 1)}{6 (x + 1) (x - 1)}$

Cancel the common factor.

$\frac{6 (x + 1) \cdot 4}{4 (3 x - 1)} \cdot \frac{16 (3 x - 1)}{6 (x + 1) (x - 1)}$

Rewrite the expression.

$\frac{4}{4 (3 x - 1)} \cdot \frac{16 (3 x - 1)}{x - 1}$

Cancel the common factor of $4 (3 x - 1)$ .

Factor $4 (3 x - 1)$ out of $16 (3 x - 1)$ .

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

Cancel the common factor.

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

Rewrite the expression.

$4 \cdot \frac{4}{x - 1}$

Combine $4$ and $\frac{4}{x - 1}$ .

$\frac{4 \cdot 4}{x - 1}$

Multiply $4$ by $4$ .

$\frac{16}{x - 1}$

Simplify (24x+24)/(12x-4)*(48x-16)/(6x^2-6)

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