Pre-Algebra Examples

$\frac{a^{2} - b^{2} - 2 a - 2 b}{4 a - 4 b - 8}$

Step 1

Factor $4$ out of $4 a - 4 b - 8$ .

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Step 1.1

Factor $4$ out of $4 a$ .

$\frac{a^{2} - b^{2} - 2 a - 2 b}{4 (a) - 4 b - 8}$

Step 1.2

Factor $4$ out of $- 4 b$ .

$\frac{a^{2} - b^{2} - 2 a - 2 b}{4 (a) + 4 (- b) - 8}$

Step 1.3

Factor $4$ out of $- 8$ .

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

Step 1.4

Factor $4$ out of $4 (a) + 4 (- b)$ .

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

Step 1.5

Factor $4$ out of $4 (a - b) + 4 (- 2)$ .

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

Step 2

Split the fraction $\frac{a^{2} - b^{2} - 2 a - 2 b}{4 (a - b - 2)}$ into two fractions.

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

Step 3

Split the fraction $\frac{a^{2} - b^{2} - 2 a}{4 (a - b - 2)}$ into two fractions.

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

Step 4

Split the fraction $\frac{a^{2} - b^{2}}{4 (a - b - 2)}$ into two fractions.

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

Step 5

Move the negative in front of the fraction.

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

Step 6

Cancel the common factor of $- 2$ and $4$ .

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Step 6.1

Factor $2$ out of $- 2 a$ .

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

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $2$ out of $4 (a - b - 2)$ .

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

Step 6.2.2

Cancel the common factor.

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

Step 6.2.3

Rewrite the expression.

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

Step 7

Move the negative in front of the fraction.

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

Step 8

Cancel the common factor of $- 2$ and $4$ .

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Step 8.1

Factor $2$ out of $- 2 b$ .

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

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $2$ out of $4 (a - b - 2)$ .

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

Step 8.2.2

Cancel the common factor.

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

Step 8.2.3

Rewrite the expression.

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

Step 9

Move the negative in front of the fraction.

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