Algebra Examples

$\frac{x + 3}{x + 4} - \frac{3 x - 6}{x^{2} + 2 x - 8}$

Step 1

Simplify each term.

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Step 1.1

Factor $3$ out of $3 x - 6$ .

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Step 1.1.1

Factor $3$ out of $3 x$ .

$\frac{x + 3}{x + 4} - \frac{3 (x) - 6}{x^{2} + 2 x - 8}$

Step 1.1.2

Factor $3$ out of $- 6$ .

$\frac{x + 3}{x + 4} - \frac{3 x + 3 \cdot - 2}{x^{2} + 2 x - 8}$

Step 1.1.3

Factor $3$ out of $3 x + 3 \cdot - 2$ .

$\frac{x + 3}{x + 4} - \frac{3 (x - 2)}{x^{2} + 2 x - 8}$

Step 1.2

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

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Step 1.2.1

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 $2$ .

$- 2, 4$

Step 1.2.2

Write the factored form using these integers.

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

Step 1.3

Cancel the common factor of $x - 2$ .

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Step 1.3.1

Cancel the common factor.

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

Step 1.3.2

Rewrite the expression.

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

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

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

Step 2.2

Combine the opposite terms in $x + 3 - 3$ .

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Step 2.2.1

Subtract $3$ from $3$ .

$\frac{x + 0}{x + 4}$

Step 2.2.2

Add $x$ and $0$ .

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