Algebra Examples

$\frac{{(x - 7)}^{2} \cdot 4 x - 2 x^{2} \cdot 2 (x - 7)}{{(x - 7)}^{4}}$

Step 1

Simplify the numerator.

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Step 1.1

Factor $(x - 7) \cdot 2 x$ out of ${(x - 7)}^{2} \cdot 4 x - 2 x^{2} \cdot (2 (x - 7))$ .

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Step 1.1.1

Factor $(x - 7) \cdot 2 x$ out of ${(x - 7)}^{2} \cdot 4 x$ .

$\frac{(x - 7) \cdot 2 x ((x - 7) \cdot 2) - 2 x^{2} \cdot (2 (x - 7))}{{(x - 7)}^{4}}$

Step 1.1.2

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

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

Step 1.1.3

Factor $(x - 7) \cdot 2 x$ out of $(x - 7) \cdot 2 x ((x - 7) \cdot 2) + (x - 7) \cdot 2 x (- x \cdot 2)$ .

$\frac{(x - 7) \cdot 2 x ((x - 7) \cdot 2 - x \cdot 2)}{{(x - 7)}^{4}}$

Step 1.2

Multiply $2$ by $- 1$ .

$\frac{(x - 7) \cdot 2 x ((x - 7) \cdot 2 - 2 x)}{{(x - 7)}^{4}}$

Step 1.3

Simplify each term.

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Step 1.3.1

Apply the distributive property.

$\frac{(x - 7) \cdot 2 x (x \cdot 2 - 7 \cdot 2 - 2 x)}{{(x - 7)}^{4}}$

Step 1.3.2

Move $2$ to the left of $x$ .

$\frac{(x - 7) \cdot 2 x (2 \cdot x - 7 \cdot 2 - 2 x)}{{(x - 7)}^{4}}$

Step 1.3.3

Multiply $- 7$ by $2$ .

$\frac{(x - 7) \cdot 2 x (2 x - 14 - 2 x)}{{(x - 7)}^{4}}$

Step 1.4

Combine the opposite terms in $2 x - 14 - 2 x$ .

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Step 1.4.1

Subtract $2 x$ from $2 x$ .

$\frac{(x - 7) \cdot 2 x (0 - 14)}{{(x - 7)}^{4}}$

Step 1.4.2

Subtract $14$ from $0$ .

$\frac{(x - 7) \cdot 2 x \cdot - 14}{{(x - 7)}^{4}}$

Step 1.5

Multiply $- 14$ by $2$ .

$\frac{(x - 7) \cdot - 28 x}{{(x - 7)}^{4}}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Cancel the common factor of $x - 7$ and ${(x - 7)}^{4}$ .

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Step 2.1.1

Factor $x - 7$ out of $(x - 7) \cdot - 28 x$ .

$\frac{(x - 7) (- 28 x)}{{(x - 7)}^{4}}$

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor $x - 7$ out of ${(x - 7)}^{4}$ .

$\frac{(x - 7) (- 28 x)}{(x - 7) {(x - 7)}^{3}}$

Step 2.1.2.2

Cancel the common factor.

$\frac{(x - 7) (- 28 x)}{(x - 7) {(x - 7)}^{3}}$

Step 2.1.2.3

Rewrite the expression.

$\frac{- 28 x}{{(x - 7)}^{3}}$

Step 2.2

Move the negative in front of the fraction.

$- \frac{28 x}{{(x - 7)}^{3}}$