Simplify (3x+24)/(x-1)*(x^2-4)/(x^2+6x-16)

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

Factor $3$ out of $3 x + 24$ .

Factor $3$ out of $3 x$ .

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

Factor $3$ out of $24$ .

$\frac{3 x + 3 \cdot 8}{x - 1} \cdot \frac{x^{2} - 4}{x^{2} + 6 x - 16}$

Factor $3$ out of $3 x + 3 \cdot 8$ .

$\frac{3 (x + 8)}{x - 1} \cdot \frac{x^{2} - 4}{x^{2} + 6 x - 16}$

Simplify the numerator.

Rewrite $4$ as $2^{2}$ .

$\frac{3 (x + 8)}{x - 1} \cdot \frac{x^{2} - 2^{2}}{x^{2} + 6 x - 16}$

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 $b = 2$ .

$\frac{3 (x + 8)}{x - 1} \cdot \frac{(x + 2) (x - 2)}{x^{2} + 6 x - 16}$

Factor $x^{2} + 6 x - 16$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 16$ and whose sum is $6$ .

$- 2, 8$

Write the factored form using these integers.

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

Simplify terms.

Cancel the common factor of $x + 8$ .

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

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

Factor $x + 8$ out of $(x - 2) (x + 8)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Cancel the common factor of $x - 2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify (3x+24)/(x-1)*(x^2-4)/(x^2+6x-16)

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