Algebra Examples

$\frac{x^{2} - 5 x - 36}{x^{2} + 10 x + 24} \cdot \frac{4 x + 24}{6 x - 54}$

Step 1

Factor $x^{2} - 5 x - 36$ 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 $- 36$ and whose sum is $- 5$ .

$- 9, 4$

Step 1.2

Write the factored form using these integers.

$\frac{(x - 9) (x + 4)}{x^{2} + 10 x + 24} \cdot \frac{4 x + 24}{6 x - 54}$

Step 2

Factor $x^{2} + 10 x + 24$ using the AC method.

Tap for more steps...

Step 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 $24$ and whose sum is $10$ .

$4, 6$

Step 2.2

Write the factored form using these integers.

$\frac{(x - 9) (x + 4)}{(x + 4) (x + 6)} \cdot \frac{4 x + 24}{6 x - 54}$

Step 3

Simplify terms.

Tap for more steps...

Step 3.1

Factor $4$ out of $4 x + 24$ .

Tap for more steps...

Step 3.1.1

Factor $4$ out of $4 x$ .

$\frac{(x - 9) (x + 4)}{(x + 4) (x + 6)} \cdot \frac{4 (x) + 24}{6 x - 54}$

Step 3.1.2

Factor $4$ out of $24$ .

$\frac{(x - 9) (x + 4)}{(x + 4) (x + 6)} \cdot \frac{4 x + 4 \cdot 6}{6 x - 54}$

Step 3.1.3

Factor $4$ out of $4 x + 4 \cdot 6$ .

$\frac{(x - 9) (x + 4)}{(x + 4) (x + 6)} \cdot \frac{4 (x + 6)}{6 x - 54}$

Step 3.2

Factor $6$ out of $6 x - 54$ .

Tap for more steps...

Step 3.2.1

Factor $6$ out of $6 x$ .

$\frac{(x - 9) (x + 4)}{(x + 4) (x + 6)} \cdot \frac{4 (x + 6)}{6 (x) - 54}$

Step 3.2.2

Factor $6$ out of $- 54$ .

$\frac{(x - 9) (x + 4)}{(x + 4) (x + 6)} \cdot \frac{4 (x + 6)}{6 x + 6 \cdot - 9}$

Step 3.2.3

Factor $6$ out of $6 x + 6 \cdot - 9$ .

$\frac{(x - 9) (x + 4)}{(x + 4) (x + 6)} \cdot \frac{4 (x + 6)}{6 (x - 9)}$

Step 3.3

Cancel the common factor of $x - 9$ .

Tap for more steps...

Step 3.3.1

Factor $x - 9$ out of $6 (x - 9)$ .

$\frac{(x - 9) (x + 4)}{(x + 4) (x + 6)} \cdot \frac{4 (x + 6)}{(x - 9) \cdot 6}$

Step 3.3.2

Cancel the common factor.

$\frac{(x - 9) (x + 4)}{(x + 4) (x + 6)} \cdot \frac{4 (x + 6)}{(x - 9) \cdot 6}$

Step 3.3.3

Rewrite the expression.

$\frac{x + 4}{(x + 4) (x + 6)} \cdot \frac{4 (x + 6)}{6}$

Step 3.4

Cancel the common factor of $x + 6$ .

Tap for more steps...

Step 3.4.1

Factor $x + 6$ out of $(x + 4) (x + 6)$ .

$\frac{x + 4}{(x + 6) (x + 4)} \cdot \frac{4 (x + 6)}{6}$

Step 3.4.2

Factor $x + 6$ out of $4 (x + 6)$ .

$\frac{x + 4}{(x + 6) (x + 4)} \cdot \frac{(x + 6) \cdot 4}{6}$

Step 3.4.3

Cancel the common factor.

$\frac{x + 4}{(x + 6) (x + 4)} \cdot \frac{(x + 6) \cdot 4}{6}$

Step 3.4.4

Rewrite the expression.

$\frac{x + 4}{x + 4} \cdot \frac{4}{6}$

Step 3.5

Multiply $\frac{x + 4}{x + 4}$ by $\frac{4}{6}$ .

$\frac{(x + 4) \cdot 4}{(x + 4) \cdot 6}$

Step 3.6

Cancel the common factor of $x + 4$ .

Tap for more steps...

Step 3.6.1

Cancel the common factor.

$\frac{(x + 4) \cdot 4}{(x + 4) \cdot 6}$

Step 3.6.2

Rewrite the expression.

$\frac{4}{6}$

Step 3.7

Cancel the common factor of $4$ and $6$ .

Tap for more steps...

Step 3.7.1

Factor $2$ out of $4$ .

$\frac{2 (2)}{6}$

Step 3.7.2

Cancel the common factors.

Tap for more steps...

Step 3.7.2.1

Factor $2$ out of $6$ .

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

Step 3.7.2.2

Cancel the common factor.

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

Step 3.7.2.3

Rewrite the expression.

$\frac{2}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{3}$

Decimal Form:

$0.\overline{6}$