Pre-Algebra Examples

$(x - 2) \div (3 x^{2} - 7 x^{2} - 8)$

Step 1

Rewrite the division as a fraction.

$\frac{x - 2}{3 x^{2} - 7 x^{2} - 8}$

Step 2

Simplify the denominator.

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Step 2.1

Subtract $7 x^{2}$ from $3 x^{2}$ .

$\frac{x - 2}{- 4 x^{2} - 8}$

Step 2.2

Factor $4$ out of $- 4 x^{2} - 8$ .

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Step 2.2.1

Factor $4$ out of $- 4 x^{2}$ .

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

Step 2.2.2

Factor $4$ out of $- 8$ .

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

Step 2.2.3

Factor $4$ out of $4 (- x^{2}) + 4 (- 2)$ .

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

Step 3

Factor $- 1$ out of $- x^{2}$ .

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

Step 4

Rewrite $- 2$ as $- 1 (2)$ .

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

Step 5

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

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

Step 6

Rewrite $- (x^{2} + 2)$ as $- 1 (x^{2} + 2)$ .

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

Step 7

Move the negative in front of the fraction.

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

Step 8

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

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

Step 9

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

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Step 9.1

Factor $2$ out of $- 2$ .

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

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $2$ out of $4 (x^{2} + 2)$ .

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

Step 9.2.2

Cancel the common factor.

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

Step 9.2.3

Rewrite the expression.

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

Step 10

Move the negative in front of the fraction.

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