Algebra Examples

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

Step 1

Simplify the numerator.

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Step 1.1

Factor $3$ out of $3 x - 6$ .

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Step 1.1.1

Factor $3$ out of $3 x$ .

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

Step 1.1.2

Factor $3$ out of $- 6$ .

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

Step 1.1.3

Factor $3$ out of $3 x + 3 \cdot - 2$ .

$\frac{{(3 (x - 2))}^{2}}{{(2 - x)}^{2}}$

Step 1.2

Apply the product rule to $3 (x - 2)$ .

$\frac{3^{2} {(x - 2)}^{2}}{{(2 - x)}^{2}}$

Step 1.3

Raise $3$ to the power of $2$ .

$\frac{9 {(x - 2)}^{2}}{{(2 - x)}^{2}}$

Step 2

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

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Step 2.1

Factor $- 1$ out of $x$ .

$\frac{9 {(- 1 (- x) - 2)}^{2}}{{(2 - x)}^{2}}$

Step 2.2

Rewrite $- 2$ as $- 1 (2)$ .

$\frac{9 {(- 1 (- x) - 1 (2))}^{2}}{{(2 - x)}^{2}}$

Step 2.3

Factor $- 1$ out of $- 1 (- x) - 1 (2)$ .

$\frac{9 {(- 1 (- x + 2))}^{2}}{{(2 - x)}^{2}}$

Step 2.4

Apply the product rule to $- 1 (- x + 2)$ .

$\frac{9 ({(- 1)}^{2} {(- x + 2)}^{2})}{{(2 - x)}^{2}}$

Step 2.5

Raise $- 1$ to the power of $2$ .

$\frac{9 (1 {(- x + 2)}^{2})}{{(2 - x)}^{2}}$

Step 2.6

Multiply ${(- x + 2)}^{2}$ by $1$ .

$\frac{9 {(- x + 2)}^{2}}{{(2 - x)}^{2}}$

Step 2.7

Reorder terms.

$\frac{9 {(- x + 2)}^{2}}{{(- x + 2)}^{2}}$

Step 2.8

Cancel the common factor.

$\frac{9 {(- x + 2)}^{2}}{{(- x + 2)}^{2}}$

Step 2.9

Divide $9$ by $1$ .

$9$