Algebra Examples

$\frac{2 a^{2} - 2}{2 a^{2} + 4 a - 6}$

Step 1

Cancel the common factor of $2 a^{2} - 2$ and $2 a^{2} + 4 a - 6$ .

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Step 1.1

Factor $2$ out of $2 a^{2}$ .

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

Step 1.2

Factor $2$ out of $- 2$ .

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

Step 1.3

Factor $2$ out of $2 (a^{2}) + 2 (- 1)$ .

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

Step 1.4

Cancel the common factors.

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Step 1.4.1

Factor $2$ out of $2 a^{2}$ .

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

Step 1.4.2

Factor $2$ out of $4 a$ .

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

Step 1.4.3

Factor $2$ out of $2 (a^{2}) + 2 (2 a)$ .

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

Step 1.4.4

Factor $2$ out of $- 6$ .

$\frac{2 (a^{2} - 1)}{2 (a^{2} + 2 a) + 2 \cdot - 3}$

Step 1.4.5

Factor $2$ out of $2 (a^{2} + 2 a) + 2 \cdot - 3$ .

$\frac{2 (a^{2} - 1)}{2 (a^{2} + 2 a - 3)}$

Step 1.4.6

Cancel the common factor.

$\frac{2 (a^{2} - 1)}{2 (a^{2} + 2 a - 3)}$

Step 1.4.7

Rewrite the expression.

$\frac{a^{2} - 1}{a^{2} + 2 a - 3}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $1$ as $1^{2}$ .

$\frac{a^{2} - 1^{2}}{a^{2} + 2 a - 3}$

Step 2.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = a$ and $b = 1$ .

$\frac{(a + 1) (a - 1)}{a^{2} + 2 a - 3}$

Step 3

Factor $a^{2} + 2 a - 3$ using the AC method.

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Step 3.1

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 $- 3$ and whose sum is $2$ .

$- 1, 3$

Step 3.2

Write the factored form using these integers.

$\frac{(a + 1) (a - 1)}{(a - 1) (a + 3)}$

Step 4

Cancel the common factor of $a - 1$ .

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Step 4.1

Cancel the common factor.

$\frac{(a + 1) (a - 1)}{(a - 1) (a + 3)}$

Step 4.2

Rewrite the expression.

$\frac{a + 1}{a + 3}$