Algebra Examples

$\frac{3 x - 6}{2 x^{2}} \div \frac{x^{2} - 5 x + 6}{4 x - 12}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{3 x - 6}{2 x^{2}} \cdot \frac{4 x - 12}{x^{2} - 5 x + 6}$

Step 2

Simplify with factoring out.

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Step 2.1

Factor $3$ out of $3 x - 6$ .

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Step 2.1.1

Factor $3$ out of $3 x$ .

$\frac{3 (x) - 6}{2 x^{2}} \cdot \frac{4 x - 12}{x^{2} - 5 x + 6}$

Step 2.1.2

Factor $3$ out of $- 6$ .

$\frac{3 x + 3 \cdot - 2}{2 x^{2}} \cdot \frac{4 x - 12}{x^{2} - 5 x + 6}$

Step 2.1.3

Factor $3$ out of $3 x + 3 \cdot - 2$ .

$\frac{3 (x - 2)}{2 x^{2}} \cdot \frac{4 x - 12}{x^{2} - 5 x + 6}$

Step 2.2

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

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Step 2.2.1

Factor $4$ out of $4 x$ .

$\frac{3 (x - 2)}{2 x^{2}} \cdot \frac{4 (x) - 12}{x^{2} - 5 x + 6}$

Step 2.2.2

Factor $4$ out of $- 12$ .

$\frac{3 (x - 2)}{2 x^{2}} \cdot \frac{4 x + 4 \cdot - 3}{x^{2} - 5 x + 6}$

Step 2.2.3

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

$\frac{3 (x - 2)}{2 x^{2}} \cdot \frac{4 (x - 3)}{x^{2} - 5 x + 6}$

Step 3

Factor $x^{2} - 5 x + 6$ 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 $6$ and whose sum is $- 5$ .

$- 3, - 2$

Step 3.2

Write the factored form using these integers.

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

Step 4

Simplify terms.

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Step 4.1

Combine.

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

Step 4.2

Cancel the common factor of $x - 2$ .

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Step 4.2.1

Cancel the common factor.

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

Step 4.2.2

Rewrite the expression.

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

Step 4.3

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

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Step 4.3.1

Factor $2$ out of $3 (4 (x - 3))$ .

$\frac{2 (3 (2 (x - 3)))}{2 x^{2} (x - 3)}$

Step 4.3.2

Cancel the common factors.

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Step 4.3.2.1

Factor $2$ out of $2 x^{2} (x - 3)$ .

$\frac{2 (3 (2 (x - 3)))}{2 (x^{2} (x - 3))}$

Step 4.3.2.2

Cancel the common factor.

$\frac{2 (3 (2 (x - 3)))}{2 (x^{2} (x - 3))}$

Step 4.3.2.3

Rewrite the expression.

$\frac{3 (2 (x - 3))}{x^{2} (x - 3)}$

Step 4.4

Cancel the common factor of $x - 3$ .

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Step 4.4.1

Cancel the common factor.

$\frac{3 (2 (x - 3))}{x^{2} (x - 3)}$

Step 4.4.2

Rewrite the expression.

$\frac{3 \cdot (2)}{x^{2}}$

Step 5

Multiply $3$ by $2$ .

$\frac{6}{x^{2}}$