Basic Math Examples

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

Step 1

Factor $k^{2} + 4 k + 3$ using the AC method.

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Step 1.1

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 $4$ .

$1, 3$

Step 1.2

Write the factored form using these integers.

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

Step 2

Factor $4$ out of $4 k - 4$ .

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Step 2.1

Factor $4$ out of $4 k$ .

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

Step 2.2

Factor $4$ out of $- 4$ .

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

Step 2.3

Factor $4$ out of $4 (k) + 4 (- 1)$ .

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

Step 3

Factor $k^{2} - k - 2$ 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 $- 2$ and whose sum is $- 1$ .

$- 2, 1$

Step 3.2

Write the factored form using these integers.

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

Step 4

Simplify terms.

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Step 4.1

Cancel the common factor of $k + 1$ .

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Step 4.1.1

Factor $k + 1$ out of $(k - 2) (k + 1)$ .

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

Step 4.1.2

Cancel the common factor.

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

Step 4.1.3

Rewrite the expression.

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

Step 4.2

Cancel the common factor of $k - 1$ .

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Step 4.2.1

Factor $k - 1$ out of $4 (k - 1)$ .

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

Step 4.3

Multiply $\frac{k + 3}{4}$ by $\frac{1}{k - 2}$ .

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