Pre-Algebra Examples

$\frac{a^{2} - b^{2} - 5 a - 5 b}{4 a - 4 b - 20}$

Step 1

Factor $4$ out of $4 a - 4 b - 20$ .

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Step 1.1

Factor $4$ out of $4 a$ .

$\frac{a^{2} - b^{2} - 5 a - 5 b}{4 (a) - 4 b - 20}$

Step 1.2

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

$\frac{a^{2} - b^{2} - 5 a - 5 b}{4 (a) + 4 (- b) - 20}$

Step 1.3

Factor $4$ out of $- 20$ .

$\frac{a^{2} - b^{2} - 5 a - 5 b}{4 (a) + 4 (- b) + 4 (- 5)}$

Step 1.4

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

$\frac{a^{2} - b^{2} - 5 a - 5 b}{4 (a - b) + 4 (- 5)}$

Step 1.5

Factor $4$ out of $4 (a - b) + 4 (- 5)$ .

$\frac{a^{2} - b^{2} - 5 a - 5 b}{4 (a - b - 5)}$

Step 2

Split the fraction $\frac{a^{2} - b^{2} - 5 a - 5 b}{4 (a - b - 5)}$ into two fractions.

$\frac{a^{2} - b^{2} - 5 a}{4 (a - b - 5)} + \frac{- 5 b}{4 (a - b - 5)}$

Step 3

Split the fraction $\frac{a^{2} - b^{2} - 5 a}{4 (a - b - 5)}$ into two fractions.

$\frac{a^{2} - b^{2}}{4 (a - b - 5)} + \frac{- 5 a}{4 (a - b - 5)} + \frac{- 5 b}{4 (a - b - 5)}$

Step 4

Split the fraction $\frac{a^{2} - b^{2}}{4 (a - b - 5)}$ into two fractions.

$\frac{a^{2}}{4 (a - b - 5)} + \frac{- b^{2}}{4 (a - b - 5)} + \frac{- 5 a}{4 (a - b - 5)} + \frac{- 5 b}{4 (a - b - 5)}$

Step 5

Move the negative in front of the fraction.

$\frac{a^{2}}{4 (a - b - 5)} - \frac{b^{2}}{4 (a - b - 5)} + \frac{- 5 a}{4 (a - b - 5)} + \frac{- 5 b}{4 (a - b - 5)}$

Step 6

Move the negative in front of the fraction.

$\frac{a^{2}}{4 (a - b - 5)} - \frac{b^{2}}{4 (a - b - 5)} - \frac{5 a}{4 (a - b - 5)} + \frac{- 5 b}{4 (a - b - 5)}$

Step 7

Move the negative in front of the fraction.

$\frac{a^{2}}{4 (a - b - 5)} - \frac{b^{2}}{4 (a - b - 5)} - \frac{5 a}{4 (a - b - 5)} - \frac{5 b}{4 (a - b - 5)}$