Pre-Algebra Examples

$R (x) = \frac{3 + 9 x}{x^{3} + 7 x^{2} - 8 x}$

Step 1

Rewrite the function as an equation.

$y = \frac{3 + 9 x}{x^{3} + 7 x^{2} - 8 x}$

Step 2

Simplify $\frac{3 + 9 x}{x^{3} + 7 x^{2} - 8 x}$ .

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Step 2.1

Factor $3$ out of $3 + 9 x$ .

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Step 2.1.1

Factor $3$ out of $3$ .

$y = \frac{3 (1) + 9 x}{x^{3} + 7 x^{2} - 8 x}$

Step 2.1.2

Factor $3$ out of $9 x$ .

$y = \frac{3 (1) + 3 (3 x)}{x^{3} + 7 x^{2} - 8 x}$

Step 2.1.3

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

$y = \frac{3 (1 + 3 x)}{x^{3} + 7 x^{2} - 8 x}$

Step 2.2

Simplify the denominator.

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Step 2.2.1

Factor $x$ out of $x^{3} + 7 x^{2} - 8 x$ .

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Step 2.2.1.1

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

$y = \frac{3 (1 + 3 x)}{x \cdot x^{2} + 7 x^{2} - 8 x}$

Step 2.2.1.2

Factor $x$ out of $7 x^{2}$ .

$y = \frac{3 (1 + 3 x)}{x \cdot x^{2} + x (7 x) - 8 x}$

Step 2.2.1.3

Factor $x$ out of $- 8 x$ .

$y = \frac{3 (1 + 3 x)}{x \cdot x^{2} + x (7 x) + x \cdot - 8}$

Step 2.2.1.4

Factor $x$ out of $x \cdot x^{2} + x (7 x)$ .

$y = \frac{3 (1 + 3 x)}{x (x^{2} + 7 x) + x \cdot - 8}$

Step 2.2.1.5

Factor $x$ out of $x (x^{2} + 7 x) + x \cdot - 8$ .

$y = \frac{3 (1 + 3 x)}{x (x^{2} + 7 x - 8)}$

Step 2.2.2

Factor $x^{2} + 7 x - 8$ using the AC method.

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Step 2.2.2.1

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 $- 8$ and whose sum is $7$ .

$- 1, 8$

Step 2.2.2.2

Write the factored form using these integers.

$y = \frac{3 (1 + 3 x)}{x ((x - 1) (x + 8))}$

$y = \frac{3 (1 + 3 x)}{x (x - 1) (x + 8)}$