Algebra Examples

$\frac{2 - x}{- 2} \cdot \frac{3 x}{x^{3} - 8 x^{2} + 12 x} \cdot \frac{x^{2} - 5 x - 6}{- x - 1}$

Step 1

Factor $x^{2} - 5 x - 6$ using the AC method.

Tap for more steps...

Step 1.1

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 $- 6$ and whose sum is $- 5$ .

$- 6, 1$

Step 1.2

Write the factored form using these integers.

$\frac{2 - x}{- 2} \cdot \frac{3 x}{x^{3} - 8 x^{2} + 12 x} \cdot \frac{(x - 6) (x + 1)}{- x - 1}$

Step 2

Simplify the denominator.

Tap for more steps...

Step 2.1

Factor $x$ out of $x^{3} - 8 x^{2} + 12 x$ .

Tap for more steps...

Step 2.1.1

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

$\frac{2 - x}{- 2} \cdot \frac{3 x}{x \cdot x^{2} - 8 x^{2} + 12 x} \cdot \frac{(x - 6) (x + 1)}{- x - 1}$

Step 2.1.2

Factor $x$ out of $- 8 x^{2}$ .

$\frac{2 - x}{- 2} \cdot \frac{3 x}{x \cdot x^{2} + x (- 8 x) + 12 x} \cdot \frac{(x - 6) (x + 1)}{- x - 1}$

Step 2.1.3

Factor $x$ out of $12 x$ .

$\frac{2 - x}{- 2} \cdot \frac{3 x}{x \cdot x^{2} + x (- 8 x) + x \cdot 12} \cdot \frac{(x - 6) (x + 1)}{- x - 1}$

Step 2.1.4

Factor $x$ out of $x \cdot x^{2} + x (- 8 x)$ .

$\frac{2 - x}{- 2} \cdot \frac{3 x}{x (x^{2} - 8 x) + x \cdot 12} \cdot \frac{(x - 6) (x + 1)}{- x - 1}$

Step 2.1.5

Factor $x$ out of $x (x^{2} - 8 x) + x \cdot 12$ .

$\frac{2 - x}{- 2} \cdot \frac{3 x}{x (x^{2} - 8 x + 12)} \cdot \frac{(x - 6) (x + 1)}{- x - 1}$

Step 2.2

Factor $x^{2} - 8 x + 12$ using the AC method.

Tap for more steps...

Step 2.2.1

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 $- 8$ .

$- 6, - 2$

Step 2.2.2

Write the factored form using these integers.

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

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

Step 3

Simplify terms.

Tap for more steps...

Step 3.1

Move the negative in front of the fraction.

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

Step 3.2

Cancel the common factor of $x$ .

Tap for more steps...

Step 3.2.1

Cancel the common factor.

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

Step 3.2.2

Rewrite the expression.

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

Step 3.3

Multiply $\frac{3}{(x - 6) (x - 2)}$ by $\frac{2 - x}{2}$ .

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

Step 3.4

Cancel the common factor of $x - 6$ .

Tap for more steps...

Step 3.4.1

Move the leading negative in $- \frac{3 (2 - x)}{(x - 6) (x - 2) \cdot 2}$ into the numerator.

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

Step 3.4.2

Factor $x - 6$ out of $(x - 6) (x - 2) \cdot 2$ .

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

Step 3.4.3

Cancel the common factor.

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

Step 3.4.4

Rewrite the expression.

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

Step 3.5

Multiply $\frac{- 3 (2 - x)}{(x - 2) \cdot 2}$ by $\frac{x + 1}{- x - 1}$ .

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

Step 3.6

Cancel the common factor of $2 - x$ and $x - 2$ .

Tap for more steps...

Step 3.6.1

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

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

Step 3.6.2

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

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

Step 3.6.3

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

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

Step 3.6.4

Reorder terms.

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

Step 3.6.5

Cancel the common factor.

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

Step 3.6.6

Rewrite the expression.

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

Step 3.7

Cancel the common factor of $x + 1$ and $- x - 1$ .

Tap for more steps...

Step 3.7.1

Factor $- 1$ out of $x$ .

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

Step 3.7.2

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

$\frac{- 3 \cdot (- 1) (- 1 (- x) - 1 (- 1))}{2 (- x - 1)}$

Step 3.7.3

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

$\frac{- 3 \cdot (- 1) (- 1 (- x - 1))}{2 (- x - 1)}$

Step 3.7.4

Cancel the common factor.

$\frac{- 3 \cdot (- 1) (- 1 (- x - 1))}{2 (- x - 1)}$

Step 3.7.5

Rewrite the expression.

$\frac{- 3 \cdot (- 1) \cdot (- 1)}{2}$

Step 4

Simplify the numerator.

Tap for more steps...

Step 4.1

Multiply $- 3$ by $- 1$ .

$\frac{3 \cdot - 1}{2}$

Step 4.2

Multiply $3$ by $- 1$ .

$\frac{- 3}{2}$

Step 5

Move the negative in front of the fraction.

$- \frac{3}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{3}{2}$

Decimal Form:

$- 1.5$

Mixed Number Form:

$- 1 \frac{1}{2}$