Algebra Examples

$1 + \frac{x^{2} + x - 6}{(x + 4) (x - 2)}$

Step 1

Simplify terms.

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Step 1.1

Simplify each term.

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Step 1.1.1

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

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Step 1.1.1.1

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 $1$ .

$- 2, 3$

Step 1.1.1.2

Write the factored form using these integers.

$1 + \frac{(x - 2) (x + 3)}{(x + 4) (x - 2)}$

Step 1.1.2

Cancel the common factor of $x - 2$ .

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Step 1.1.2.1

Cancel the common factor.

$1 + \frac{(x - 2) (x + 3)}{(x + 4) (x - 2)}$

Step 1.1.2.2

Rewrite the expression.

$1 + \frac{x + 3}{x + 4}$

Step 1.2

Combine into one fraction.

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Step 1.2.1

Write $1$ as a fraction with a common denominator.

$\frac{x + 4}{x + 4} + \frac{x + 3}{x + 4}$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{x + 4 + x + 3}{x + 4}$

Step 2

Simplify the numerator.

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Step 2.1

Add $x$ and $x$ .

$\frac{2 x + 4 + 3}{x + 4}$

Step 2.2

Add $4$ and $3$ .

$\frac{2 x + 7}{x + 4}$