Pre-Algebra Examples

$\frac{x^{2} + x - 6}{x - 1} \div \frac{4 x - 8}{x + 1}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{x^{2} + x - 6}{x - 1} \cdot \frac{x + 1}{4 x - 8}$

Step 2

Factor $x^{2} + x - 6$ using the AC method.

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Step 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 $- 6$ and whose sum is $1$ .

$- 2, 3$

Step 2.2

Write the factored form using these integers.

$\frac{(x - 2) (x + 3)}{x - 1} \cdot \frac{x + 1}{4 x - 8}$

Step 3

Factor $4$ out of $4 x - 8$ .

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Step 3.1

Factor $4$ out of $4 x$ .

$\frac{(x - 2) (x + 3)}{x - 1} \cdot \frac{x + 1}{4 (x) - 8}$

Step 3.2

Factor $4$ out of $- 8$ .

$\frac{(x - 2) (x + 3)}{x - 1} \cdot \frac{x + 1}{4 x + 4 \cdot - 2}$

Step 3.3

Factor $4$ out of $4 x + 4 \cdot - 2$ .

$\frac{(x - 2) (x + 3)}{x - 1} \cdot \frac{x + 1}{4 (x - 2)}$

Step 4

Cancel the common factor of $x - 2$ .

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Step 4.1

Factor $x - 2$ out of $4 (x - 2)$ .

$\frac{(x - 2) (x + 3)}{x - 1} \cdot \frac{x + 1}{(x - 2) \cdot 4}$

Step 4.2

Cancel the common factor.

$\frac{(x - 2) (x + 3)}{x - 1} \cdot \frac{x + 1}{(x - 2) \cdot 4}$

Step 4.3

Rewrite the expression.

$\frac{x + 3}{x - 1} \cdot \frac{x + 1}{4}$

Step 5

Multiply $\frac{x + 3}{x - 1}$ by $\frac{x + 1}{4}$ .

$\frac{(x + 3) (x + 1)}{(x - 1) \cdot 4}$

Step 6

Move $4$ to the left of $x - 1$ .

$\frac{(x + 3) (x + 1)}{4 (x - 1)}$