Simplify (x^3-x^2-42x)/(2x^2-20x+42)

$\frac{x^{3} - x^{2} - 42 x}{2 x^{2} - 20 x + 42}$

Simplify the numerator.

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Factor $x$ out of $x^{3} - x^{2} - 42 x$ .

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Factor $x$ out of $x^{3}$ .

$\frac{x \cdot x^{2} - x^{2} - 42 x}{2 x^{2} - 20 x + 42}$

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

$\frac{x \cdot x^{2} + x (- x) - 42 x}{2 x^{2} - 20 x + 42}$

Factor $x$ out of $- 42 x$ .

$\frac{x \cdot x^{2} + x (- x) + x \cdot - 42}{2 x^{2} - 20 x + 42}$

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

$\frac{x (x^{2} - x) + x \cdot - 42}{2 x^{2} - 20 x + 42}$

Factor $x$ out of $x (x^{2} - x) + x \cdot - 42$ .

$\frac{x (x^{2} - x - 42)}{2 x^{2} - 20 x + 42}$

Factor $x^{2} - x - 42$ using the AC method.

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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 $- 42$ and whose sum is $- 1$ .

$- 7, 6$

Write the factored form using these integers.

$\frac{x ((x - 7) (x + 6))}{2 x^{2} - 20 x + 42}$

$\frac{x (x - 7) (x + 6)}{2 x^{2} - 20 x + 42}$

Simplify the denominator.

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Factor $2$ out of $2 x^{2} - 20 x + 42$ .

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

$\frac{x (x - 7) (x + 6)}{2 (x^{2}) - 20 x + 42}$

Factor $2$ out of $- 20 x$ .

$\frac{x (x - 7) (x + 6)}{2 (x^{2}) + 2 (- 10 x) + 42}$

Factor $2$ out of $42$ .

$\frac{x (x - 7) (x + 6)}{2 x^{2} + 2 (- 10 x) + 2 \cdot 21}$

Factor $2$ out of $2 x^{2} + 2 (- 10 x)$ .

$\frac{x (x - 7) (x + 6)}{2 (x^{2} - 10 x) + 2 \cdot 21}$

Factor $2$ out of $2 (x^{2} - 10 x) + 2 \cdot 21$ .

$\frac{x (x - 7) (x + 6)}{2 (x^{2} - 10 x + 21)}$

Factor $x^{2} - 10 x + 21$ using the AC method.

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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 $21$ and whose sum is $- 10$ .

$- 7, - 3$

Write the factored form using these integers.

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

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

Cancel the common factor of $x - 7$ .

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Cancel the common factor.

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

Rewrite the expression.

$\frac{x (x + 6)}{2 (x - 3)}$

Simplify (x^3-x^2-42x)/(2x^2-20x+42)

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