Algebra Examples

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

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

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

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

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Step 1.1.1.1

Consider the form

x^{2} + b x + c

$x^{2} + b x + c$ . Find a pair of integers whose product is

c

$c$ and whose sum is

b

$b$ . In this case, whose product is

- 6

$- 6$ and whose sum is

1

$1$ .

- 2, 3

$- 2, 3$

Step 1.1.1.2

Write the factored form using these integers.

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

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

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

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

Step 1.1.2

Cancel the common factor of

x - 2

$x - 2$ .

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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

$3$ .

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