Simplify (4x^2-24x)/(4x^4+12x^3-16x^2)*(x^2-9x+8)/(x^2-14x+48)

$\frac{4 x^{2} - 24 x}{4 x^{4} + 12 x^{3} - 16 x^{2}} \cdot \frac{x^{2} - 9 x + 8}{x^{2} - 14 x + 48}$

Factor $4 x$ out of $4 x^{2} - 24 x$ .

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

$\frac{4 x (x) - 24 x}{4 x^{4} + 12 x^{3} - 16 x^{2}} \cdot \frac{x^{2} - 9 x + 8}{x^{2} - 14 x + 48}$

Factor $4 x$ out of $- 24 x$ .

$\frac{4 x (x) + 4 x (- 6)}{4 x^{4} + 12 x^{3} - 16 x^{2}} \cdot \frac{x^{2} - 9 x + 8}{x^{2} - 14 x + 48}$

Factor $4 x$ out of $4 x (x) + 4 x (- 6)$ .

$\frac{4 x (x - 6)}{4 x^{4} + 12 x^{3} - 16 x^{2}} \cdot \frac{x^{2} - 9 x + 8}{x^{2} - 14 x + 48}$

Simplify the denominator.

Factor $4 x^{2}$ out of $4 x^{4} + 12 x^{3} - 16 x^{2}$ .

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

$\frac{4 x (x - 6)}{4 x^{2} (x^{2}) + 12 x^{3} - 16 x^{2}} \cdot \frac{x^{2} - 9 x + 8}{x^{2} - 14 x + 48}$

Factor $4 x^{2}$ out of $12 x^{3}$ .

$\frac{4 x (x - 6)}{4 x^{2} (x^{2}) + 4 x^{2} (3 x) - 16 x^{2}} \cdot \frac{x^{2} - 9 x + 8}{x^{2} - 14 x + 48}$

Factor $4 x^{2}$ out of $- 16 x^{2}$ .

$\frac{4 x (x - 6)}{4 x^{2} (x^{2}) + 4 x^{2} (3 x) + 4 x^{2} (- 4)} \cdot \frac{x^{2} - 9 x + 8}{x^{2} - 14 x + 48}$

Factor $4 x^{2}$ out of $4 x^{2} (x^{2}) + 4 x^{2} (3 x)$ .

$\frac{4 x (x - 6)}{4 x^{2} (x^{2} + 3 x) + 4 x^{2} (- 4)} \cdot \frac{x^{2} - 9 x + 8}{x^{2} - 14 x + 48}$

Factor $4 x^{2}$ out of $4 x^{2} (x^{2} + 3 x) + 4 x^{2} (- 4)$ .

$\frac{4 x (x - 6)}{4 x^{2} (x^{2} + 3 x - 4)} \cdot \frac{x^{2} - 9 x + 8}{x^{2} - 14 x + 48}$

Factor $x^{2} + 3 x - 4$ 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 $- 4$ and whose sum is $3$ .

$- 1, 4$

Write the factored form using these integers.

$\frac{4 x (x - 6)}{4 x^{2} ((x - 1) (x + 4))} \cdot \frac{x^{2} - 9 x + 8}{x^{2} - 14 x + 48}$

$\frac{4 x (x - 6)}{4 x^{2} (x - 1) (x + 4)} \cdot \frac{x^{2} - 9 x + 8}{x^{2} - 14 x + 48}$

Factor $x^{2} - 9 x + 8$ 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 $- 9$ .

$- 8, - 1$

Write the factored form using these integers.

$\frac{4 x (x - 6)}{4 x^{2} (x - 1) (x + 4)} \cdot \frac{(x - 8) (x - 1)}{x^{2} - 14 x + 48}$

Factor $x^{2} - 14 x + 48$ 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 $48$ and whose sum is $- 14$ .

$- 8, - 6$

Write the factored form using these integers.

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

Simplify terms.

Combine.

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

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

Factor $x$ out of $(x (x - 6)) ((x - 8) (x - 1))$ .

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

Cancel the common factors.

Factor $x$ out of $((x^{2} (x - 1)) (x + 4)) ((x - 8) (x - 6))$ .

$\frac{x ((x - 6) ((x - 8) (x - 1)))}{x (((x (x - 1)) (x + 4)) ((x - 8) (x - 6)))}$

Cancel the common factor.

$\frac{x ((x - 6) ((x - 8) (x - 1)))}{x (((x (x - 1)) (x + 4)) ((x - 8) (x - 6)))}$

Rewrite the expression.

$\frac{(x - 6) ((x - 8) (x - 1))}{((x (x - 1)) (x + 4)) ((x - 8) (x - 6))}$

Cancel the common factor of $x - 6$ .

Cancel the common factor.

$\frac{(x - 6) ((x - 8) (x - 1))}{(x (x - 1)) (x + 4) ((x - 8) (x - 6))}$

Rewrite the expression.

$\frac{(x - 8) (x - 1)}{((x (x - 1)) (x + 4)) (x - 8)}$

Cancel the common factor of $x - 8$ .

Cancel the common factor.

$\frac{(x - 8) (x - 1)}{(x (x - 1)) (x + 4) (x - 8)}$

Rewrite the expression.

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

Cancel the common factor of $x - 1$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{(x) (x + 4)}$

$\frac{1}{x (x + 4)}$

Simplify (4x^2-24x)/(4x^4+12x^3-16x^2)*(x^2-9x+8)/(x^2-14x+48)

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