Pre-Algebra Examples

$\frac{x^{2} + 3 x + 2}{x^{2} - 4 x + 3} \div \frac{x + 1}{4 x - 12}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{x^{2} + 3 x + 2}{x^{2} - 4 x + 3} \cdot \frac{4 x - 12}{x + 1}$

Step 2

Factor $x^{2} + 3 x + 2$ 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 $2$ and whose sum is $3$ .

$1, 2$

Step 2.2

Write the factored form using these integers.

$\frac{(x + 1) (x + 2)}{x^{2} - 4 x + 3} \cdot \frac{4 x - 12}{x + 1}$

Step 3

Factor $x^{2} - 4 x + 3$ 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 $- 4$ .

$- 3, - 1$

Step 3.2

Write the factored form using these integers.

$\frac{(x + 1) (x + 2)}{(x - 3) (x - 1)} \cdot \frac{4 x - 12}{x + 1}$

Step 4

Cancel the common factor of $x + 1$ .

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Step 4.1

Cancel the common factor.

$\frac{(x + 1) (x + 2)}{(x - 3) (x - 1)} \cdot \frac{4 x - 12}{x + 1}$

Step 4.2

Rewrite the expression.

$\frac{x + 2}{(x - 3) (x - 1)} (4 x - 12)$

Step 5

Multiply $\frac{x + 2}{(x - 3) (x - 1)}$ by $4 x - 12$ .

$\frac{(x + 2) (4 x - 12)}{(x - 3) (x - 1)}$

Step 6

Factor $4$ out of $4 x - 12$ .

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Step 6.1

Factor $4$ out of $4 x$ .

$\frac{(x + 2) (4 (x) - 12)}{(x - 3) (x - 1)}$

Step 6.2

Factor $4$ out of $- 12$ .

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

Step 6.3

Factor $4$ out of $4 x + 4 \cdot - 3$ .

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

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

Step 7

Cancel the common factor of $x - 3$ .

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Step 7.1

Cancel the common factor.

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

Step 7.2

Rewrite the expression.

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

Step 8

Move $4$ to the left of $x + 2$ .

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