Simplify (6x^2-384)/(x^4-15x^3+56x^2)*(x^4-8x^3+7x^2)/(x^2+7x-8)

$\frac{6 x^{2} - 384}{x^{4} - 15 x^{3} + 56 x^{2}} \cdot \frac{x^{4} - 8 x^{3} + 7 x^{2}}{x^{2} + 7 x - 8}$

Simplify the numerator.

Factor $6$ out of $6 x^{2} - 384$ .

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

$\frac{6 (x^{2}) - 384}{x^{4} - 15 x^{3} + 56 x^{2}} \cdot \frac{x^{4} - 8 x^{3} + 7 x^{2}}{x^{2} + 7 x - 8}$

Factor $6$ out of $- 384$ .

$\frac{6 x^{2} + 6 \cdot - 64}{x^{4} - 15 x^{3} + 56 x^{2}} \cdot \frac{x^{4} - 8 x^{3} + 7 x^{2}}{x^{2} + 7 x - 8}$

Factor $6$ out of $6 x^{2} + 6 \cdot - 64$ .

$\frac{6 (x^{2} - 64)}{x^{4} - 15 x^{3} + 56 x^{2}} \cdot \frac{x^{4} - 8 x^{3} + 7 x^{2}}{x^{2} + 7 x - 8}$

Rewrite $64$ as $8^{2}$ .

$\frac{6 (x^{2} - 8^{2})}{x^{4} - 15 x^{3} + 56 x^{2}} \cdot \frac{x^{4} - 8 x^{3} + 7 x^{2}}{x^{2} + 7 x - 8}$

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 $b = 8$ .

$\frac{6 (x + 8) (x - 8)}{x^{4} - 15 x^{3} + 56 x^{2}} \cdot \frac{x^{4} - 8 x^{3} + 7 x^{2}}{x^{2} + 7 x - 8}$

Simplify the denominator.

Factor $x^{2}$ out of $x^{4} - 15 x^{3} + 56 x^{2}$ .

Factor $x^{2}$ out of $x^{4}$ .

$\frac{6 (x + 8) (x - 8)}{x^{2} x^{2} - 15 x^{3} + 56 x^{2}} \cdot \frac{x^{4} - 8 x^{3} + 7 x^{2}}{x^{2} + 7 x - 8}$

Factor $x^{2}$ out of $- 15 x^{3}$ .

$\frac{6 (x + 8) (x - 8)}{x^{2} x^{2} + x^{2} (- 15 x) + 56 x^{2}} \cdot \frac{x^{4} - 8 x^{3} + 7 x^{2}}{x^{2} + 7 x - 8}$

Factor $x^{2}$ out of $56 x^{2}$ .

$\frac{6 (x + 8) (x - 8)}{x^{2} x^{2} + x^{2} (- 15 x) + x^{2} \cdot 56} \cdot \frac{x^{4} - 8 x^{3} + 7 x^{2}}{x^{2} + 7 x - 8}$

Factor $x^{2}$ out of $x^{2} x^{2} + x^{2} (- 15 x)$ .

$\frac{6 (x + 8) (x - 8)}{x^{2} (x^{2} - 15 x) + x^{2} \cdot 56} \cdot \frac{x^{4} - 8 x^{3} + 7 x^{2}}{x^{2} + 7 x - 8}$

Factor $x^{2}$ out of $x^{2} (x^{2} - 15 x) + x^{2} \cdot 56$ .

$\frac{6 (x + 8) (x - 8)}{x^{2} (x^{2} - 15 x + 56)} \cdot \frac{x^{4} - 8 x^{3} + 7 x^{2}}{x^{2} + 7 x - 8}$

Factor $x^{2} - 15 x + 56$ 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 $56$ and whose sum is $- 15$ .

$- 8, - 7$

Write the factored form using these integers.

$\frac{6 (x + 8) (x - 8)}{x^{2} ((x - 8) (x - 7))} \cdot \frac{x^{4} - 8 x^{3} + 7 x^{2}}{x^{2} + 7 x - 8}$

$\frac{6 (x + 8) (x - 8)}{x^{2} (x - 8) (x - 7)} \cdot \frac{x^{4} - 8 x^{3} + 7 x^{2}}{x^{2} + 7 x - 8}$

Simplify the numerator.

Factor $x^{2}$ out of $x^{4} - 8 x^{3} + 7 x^{2}$ .

Factor $x^{2}$ out of $x^{4}$ .

$\frac{6 (x + 8) (x - 8)}{x^{2} (x - 8) (x - 7)} \cdot \frac{x^{2} x^{2} - 8 x^{3} + 7 x^{2}}{x^{2} + 7 x - 8}$

Factor $x^{2}$ out of $- 8 x^{3}$ .

$\frac{6 (x + 8) (x - 8)}{x^{2} (x - 8) (x - 7)} \cdot \frac{x^{2} x^{2} + x^{2} (- 8 x) + 7 x^{2}}{x^{2} + 7 x - 8}$

Factor $x^{2}$ out of $7 x^{2}$ .

$\frac{6 (x + 8) (x - 8)}{x^{2} (x - 8) (x - 7)} \cdot \frac{x^{2} x^{2} + x^{2} (- 8 x) + x^{2} \cdot 7}{x^{2} + 7 x - 8}$

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

$\frac{6 (x + 8) (x - 8)}{x^{2} (x - 8) (x - 7)} \cdot \frac{x^{2} (x^{2} - 8 x) + x^{2} \cdot 7}{x^{2} + 7 x - 8}$

Factor $x^{2}$ out of $x^{2} (x^{2} - 8 x) + x^{2} \cdot 7$ .

$\frac{6 (x + 8) (x - 8)}{x^{2} (x - 8) (x - 7)} \cdot \frac{x^{2} (x^{2} - 8 x + 7)}{x^{2} + 7 x - 8}$

Factor $x^{2} - 8 x + 7$ 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 $7$ and whose sum is $- 8$ .

$- 7, - 1$

Write the factored form using these integers.

$\frac{6 (x + 8) (x - 8)}{x^{2} (x - 8) (x - 7)} \cdot \frac{x^{2} ((x - 7) (x - 1))}{x^{2} + 7 x - 8}$

$\frac{6 (x + 8) (x - 8)}{x^{2} (x - 8) (x - 7)} \cdot \frac{x^{2} (x - 7) (x - 1)}{x^{2} + 7 x - 8}$

Factor $x^{2} + 7 x - 8$ 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 $- 8$ and whose sum is $7$ .

$- 1, 8$

Write the factored form using these integers.

$\frac{6 (x + 8) (x - 8)}{x^{2} (x - 8) (x - 7)} \cdot \frac{x^{2} (x - 7) (x - 1)}{(x - 1) (x + 8)}$

Simplify terms.

Combine.

$\frac{6 (x + 8) (x - 8) (x^{2} (x - 7) (x - 1))}{x^{2} (x - 8) (x - 7) ((x - 1) (x + 8))}$

Cancel the common factor of $x + 8$ .

Cancel the common factor.

$\frac{6 (x + 8) (x - 8) (x^{2} (x - 7) (x - 1))}{x^{2} (x - 8) (x - 7) ((x - 1) (x + 8))}$

Rewrite the expression.

$\frac{(6 (x - 8)) (x^{2} (x - 7) (x - 1))}{x^{2} (x - 8) (x - 7) (x - 1)}$

Cancel the common factor of $x - 8$ .

Cancel the common factor.

$\frac{6 (x - 8) (x^{2} (x - 7) (x - 1))}{x^{2} (x - 8) (x - 7) (x - 1)}$

Rewrite the expression.

$\frac{(6) (x^{2} (x - 7) (x - 1))}{(x^{2} (x - 7)) (x - 1)}$

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

Cancel the common factor.

$\frac{6 (x^{2} (x - 7) (x - 1))}{x^{2} (x - 7) (x - 1)}$

Rewrite the expression.

$\frac{(6) ((x - 7) (x - 1))}{(x - 7) (x - 1)}$

Cancel the common factor of $x - 7$ .

Cancel the common factor.

$\frac{6 ((x - 7) (x - 1))}{(x - 7) (x - 1)}$

Rewrite the expression.

$\frac{(6) (x - 1)}{x - 1}$

Cancel the common factor of $x - 1$ .

Cancel the common factor.

$\frac{6 (x - 1)}{x - 1}$

Divide $6$ by $1$ .

$6$

Simplify (6x^2-384)/(x^4-15x^3+56x^2)*(x^4-8x^3+7x^2)/(x^2+7x-8)

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