Algebra Examples

$\frac{x^{3} (x + 5)}{x - 9} \cdot \frac{(x - 9) (x + 8)}{3 x^{3}}$

Step 1

Simplify terms.

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Step 1.1

Cancel the common factor of $x^{3}$ .

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Step 1.1.1

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

$\frac{x^{3} (x + 5)}{x - 9} \cdot \frac{(x - 9) (x + 8)}{x^{3} \cdot 3}$

Step 1.1.2

Cancel the common factor.

$\frac{x^{3} (x + 5)}{x - 9} \cdot \frac{(x - 9) (x + 8)}{x^{3} \cdot 3}$

Step 1.1.3

Rewrite the expression.

$\frac{x + 5}{x - 9} \cdot \frac{(x - 9) (x + 8)}{3}$

Step 1.2

Simplify terms.

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Step 1.2.1

Cancel the common factor of $x - 9$ .

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Step 1.2.1.1

Rewrite.

$\frac{x + 5}{x - 9} \cdot \frac{(x - 9) (x + 8)}{3}$

Step 1.2.1.2

Cancel the common factor.

$\frac{x + 5}{x - 9} \cdot \frac{(x - 9) (x + 8)}{3}$

Step 1.2.1.3

Rewrite the expression.

$(x + 5) \cdot \frac{x + 8}{3}$

Step 1.2.2

Apply the distributive property.

$x \frac{x + 8}{3} + 5 \frac{x + 8}{3}$

Step 1.2.3

Combine $x$ and $\frac{x + 8}{3}$ .

$\frac{x (x + 8)}{3} + 5 \frac{x + 8}{3}$

Step 1.2.4

Combine $5$ and $\frac{x + 8}{3}$ .

$\frac{x (x + 8)}{3} + \frac{5 (x + 8)}{3}$

Step 1.2.5

Combine the numerators over the common denominator.

$\frac{x (x + 8) + 5 (x + 8)}{3}$

Step 1.3

Simplify each term.

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Step 1.3.1

Apply the distributive property.

$\frac{x \cdot x + x \cdot 8 + 5 (x + 8)}{3}$

Step 1.3.2

Multiply $x$ by $x$ .

$\frac{x^{2} + x \cdot 8 + 5 (x + 8)}{3}$

Step 1.3.3

Move $8$ to the left of $x$ .

$\frac{x^{2} + 8 \cdot x + 5 (x + 8)}{3}$

Step 1.3.4

Apply the distributive property.

$\frac{x^{2} + 8 x + 5 x + 5 \cdot 8}{3}$

Step 1.3.5

Multiply $5$ by $8$ .

$\frac{x^{2} + 8 x + 5 x + 40}{3}$

Step 1.4

Add $8 x$ and $5 x$ .

$\frac{x^{2} + 13 x + 40}{3}$

Step 2

Factor $x^{2} + 13 x + 40$ using the AC method.

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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 $40$ and whose sum is $13$ .

$5, 8$

Step 2.2

Write the factored form using these integers.

$\frac{(x + 5) (x + 8)}{3}$