Simplify (4x-16)/x*(x^2-11x+24)/(x^2-7x+12)

$\frac{4 x - 16}{x} \cdot \frac{x^{2} - 11 x + 24}{x^{2} - 7 x + 12}$

Step 1

Factor $4$ out of $4 x - 16$ .

Factor $4$ out of $4 x$ .

$\frac{4 (x) - 16}{x} \cdot \frac{x^{2} - 11 x + 24}{x^{2} - 7 x + 12}$

Factor $4$ out of $- 16$ .

$\frac{4 x + 4 \cdot - 4}{x} \cdot \frac{x^{2} - 11 x + 24}{x^{2} - 7 x + 12}$

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

$\frac{4 (x - 4)}{x} \cdot \frac{x^{2} - 11 x + 24}{x^{2} - 7 x + 12}$

Step 2

Factor $x^{2} - 11 x + 24$ 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 $24$ and whose sum is $- 11$ .

$- 8, - 3$

Write the factored form using these integers.

$\frac{4 (x - 4)}{x} \cdot \frac{(x - 8) (x - 3)}{x^{2} - 7 x + 12}$

Step 3

Factor $x^{2} - 7 x + 12$ 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 $12$ and whose sum is $- 7$ .

$- 4, - 3$

Write the factored form using these integers.

$\frac{4 (x - 4)}{x} \cdot \frac{(x - 8) (x - 3)}{(x - 4) (x - 3)}$

Step 4

Simplify terms.

Cancel the common factor of $x - 4$ .

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

$\frac{(x - 4) \cdot 4}{x} \cdot \frac{(x - 8) (x - 3)}{(x - 4) (x - 3)}$

Cancel the common factor.

$\frac{(x - 4) \cdot 4}{x} \cdot \frac{(x - 8) (x - 3)}{(x - 4) (x - 3)}$

Rewrite the expression.

$\frac{4}{x} \cdot \frac{(x - 8) (x - 3)}{x - 3}$

Multiply $\frac{4}{x}$ by $\frac{(x - 8) (x - 3)}{x - 3}$ .

$\frac{4 ((x - 8) (x - 3))}{x (x - 3)}$

Cancel the common factor of $x - 3$ .

Cancel the common factor.

$\frac{4 ((x - 8) (x - 3))}{x (x - 3)}$

Rewrite the expression.

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

Simplify (4x-16)/x*(x^2-11x+24)/(x^2-7x+12)

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