Algebra Examples

$\frac{54 {(x - 3)}^{3}}{63 {(3 - x)}^{2}}$

Step 1

Cancel the common factor of $54$ and $63$ .

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Step 1.1

Factor $9$ out of $54 {(x - 3)}^{3}$ .

$\frac{9 (6 {(x - 3)}^{3})}{63 {(3 - x)}^{2}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $9$ out of $63 {(3 - x)}^{2}$ .

$\frac{9 (6 {(x - 3)}^{3})}{9 (7 {(3 - x)}^{2})}$

Step 1.2.2

Cancel the common factor.

$\frac{9 (6 {(x - 3)}^{3})}{9 (7 {(3 - x)}^{2})}$

Step 1.2.3

Rewrite the expression.

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

Step 2

Cancel the common factor of ${(x - 3)}^{3}$ and ${(3 - x)}^{2}$ .

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Step 2.1

Factor $- 1$ out of $x$ .

$\frac{6 {(- 1 (- x) - 3)}^{3}}{7 {(3 - x)}^{2}}$

Step 2.2

Rewrite $- 3$ as $- 1 (3)$ .

$\frac{6 {(- 1 (- x) - 1 (3))}^{3}}{7 {(3 - x)}^{2}}$

Step 2.3

Factor $- 1$ out of $- 1 (- x) - 1 (3)$ .

$\frac{6 {(- 1 (- x + 3))}^{3}}{7 {(3 - x)}^{2}}$

Step 2.4

Apply the product rule to $- 1 (- x + 3)$ .

$\frac{6 ({(- 1)}^{3} {(- x + 3)}^{3})}{7 {(3 - x)}^{2}}$

Step 2.5

Raise $- 1$ to the power of $3$ .

$\frac{6 (- 1 {(- x + 3)}^{3})}{7 {(3 - x)}^{2}}$

Step 2.6

Reorder terms.

$\frac{6 (- 1 {(- x + 3)}^{3})}{7 {(- x + 3)}^{2}}$

Step 2.7

Factor ${(- x + 3)}^{2}$ out of $6 (- 1 {(- x + 3)}^{3})$ .

$\frac{{(- x + 3)}^{2} (6 (- 1 (- x + 3)))}{7 {(- x + 3)}^{2}}$

Step 2.8

Cancel the common factors.

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Step 2.8.1

Factor ${(- x + 3)}^{2}$ out of $7 {(- x + 3)}^{2}$ .

$\frac{{(- x + 3)}^{2} (6 (- 1 (- x + 3)))}{{(- x + 3)}^{2} \cdot 7}$

Step 2.8.2

Cancel the common factor.

$\frac{{(- x + 3)}^{2} (6 (- 1 (- x + 3)))}{{(- x + 3)}^{2} \cdot 7}$

Step 2.8.3

Rewrite the expression.

$\frac{6 (- 1 (- x + 3))}{7}$

Step 3

Simplify the expression.

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Step 3.1

Multiply $- 1$ by $6$ .

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

Step 3.2

Move the negative in front of the fraction.

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

Step 4

Factor $- 1$ out of $- x$ .

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

Step 5

Rewrite $3$ as $- 1 (- 3)$ .

$- \frac{6 (- (x) - 1 (- 3))}{7}$

Step 6

Factor $- 1$ out of $- (x) - 1 (- 3)$ .

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

Step 7

Simplify the expression.

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Step 7.1

Rewrite $- (x - 3)$ as $- 1 (x - 3)$ .

$- \frac{6 (- 1 (x - 3))}{7}$

Step 7.2

Move the negative in front of the fraction.

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

Step 7.3

Multiply $- 1$ by $- 1$ .

$1 \frac{6 (x - 3)}{7}$

Step 7.4

Multiply $\frac{6 (x - 3)}{7}$ by $1$ .

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