Basic Math Examples

$\frac{k^{2} - 5 k + 4}{2 k - 8} \div (3 k^{2} - 3 k)$

Step 1

Rewrite the division as a fraction.

$\frac{\frac{k^{2} - 5 k + 4}{2 k - 8}}{3 k^{2} - 3 k}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{k^{2} - 5 k + 4}{2 k - 8} \cdot \frac{1}{3 k^{2} - 3 k}$

Step 3

Factor $k^{2} - 5 k + 4$ 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 $4$ and whose sum is $- 5$ .

$- 4, - 1$

Step 3.2

Write the factored form using these integers.

$\frac{(k - 4) (k - 1)}{2 k - 8} \cdot \frac{1}{3 k^{2} - 3 k}$

Step 4

Simplify terms.

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Step 4.1

Factor $2$ out of $2 k - 8$ .

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Step 4.1.1

Factor $2$ out of $2 k$ .

$\frac{(k - 4) (k - 1)}{2 (k) - 8} \cdot \frac{1}{3 k^{2} - 3 k}$

Step 4.1.2

Factor $2$ out of $- 8$ .

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

Step 4.1.3

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

$\frac{(k - 4) (k - 1)}{2 (k - 4)} \cdot \frac{1}{3 k^{2} - 3 k}$

Step 4.2

Cancel the common factor of $k - 4$ .

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Step 4.2.1

Cancel the common factor.

$\frac{(k - 4) (k - 1)}{2 (k - 4)} \cdot \frac{1}{3 k^{2} - 3 k}$

Step 4.2.2

Rewrite the expression.

$\frac{k - 1}{2} \cdot \frac{1}{3 k^{2} - 3 k}$

Step 4.3

Factor $3 k$ out of $3 k^{2} - 3 k$ .

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Step 4.3.1

Factor $3 k$ out of $3 k^{2}$ .

$\frac{k - 1}{2} \cdot \frac{1}{3 k (k) - 3 k}$

Step 4.3.2

Factor $3 k$ out of $- 3 k$ .

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

Step 4.3.3

Factor $3 k$ out of $3 k (k) + 3 k (- 1)$ .

$\frac{k - 1}{2} \cdot \frac{1}{3 k (k - 1)}$

Step 4.4

Cancel the common factor of $k - 1$ .

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Step 4.4.1

Factor $k - 1$ out of $3 k (k - 1)$ .

$\frac{k - 1}{2} \cdot \frac{1}{(k - 1) (3 k)}$

Step 4.4.2

Cancel the common factor.

$\frac{k - 1}{2} \cdot \frac{1}{(k - 1) (3 k)}$

Step 4.4.3

Rewrite the expression.

$\frac{1}{2} \cdot \frac{1}{3 k}$

Step 4.5

Multiply $\frac{1}{2}$ by $\frac{1}{3 k}$ .

$\frac{1}{2 (3 k)}$

Step 4.6

Multiply $3$ by $2$ .

$\frac{1}{6 k}$