Algebra Examples

$\frac{x^{2} + x + 2}{x + 4} - \frac{2 x + 22}{x + 4}$

Step 1

Simplify terms.

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Step 1.1

Combine the numerators over the common denominator.

$\frac{x^{2} + x + 2 - (2 x + 22)}{x + 4}$

Step 1.2

Simplify each term.

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Step 1.2.1

Apply the distributive property.

$\frac{x^{2} + x + 2 - (2 x) - 1 \cdot 22}{x + 4}$

Step 1.2.2

Multiply $2$ by $- 1$ .

$\frac{x^{2} + x + 2 - 2 x - 1 \cdot 22}{x + 4}$

Step 1.2.3

Multiply $- 1$ by $22$ .

$\frac{x^{2} + x + 2 - 2 x - 22}{x + 4}$

Step 1.3

Simplify by adding terms.

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Step 1.3.1

Subtract $2 x$ from $x$ .

$\frac{x^{2} - x + 2 - 22}{x + 4}$

Step 1.3.2

Subtract $22$ from $2$ .

$\frac{x^{2} - x - 20}{x + 4}$

Step 2

Factor $x^{2} - x - 20$ 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 $- 20$ and whose sum is $- 1$ .

$- 5, 4$

Step 2.2

Write the factored form using these integers.

$\frac{(x - 5) (x + 4)}{x + 4}$

Step 3

Cancel the common factor of $x + 4$ .

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Step 3.1

Cancel the common factor.

$\frac{(x - 5) (x + 4)}{x + 4}$

Step 3.2

Divide $x - 5$ by $1$ .

$x - 5$