Finite Math Examples

$\frac{k + (k - 1) - 1}{k ((k + 1) \cdot 0 + (k - 1) - 1) - 1}$

Step 1

Remove parentheses.

$\frac{k + k - 1 - 1}{k ((k + 1) \cdot 0 + k - 1 - 1) - 1}$

Step 2

Simplify the numerator.

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Step 2.1

Add $k$ and $k$ .

$\frac{2 k - 1 - 1}{k ((k + 1) \cdot 0 + k - 1 - 1) - 1}$

Step 2.2

Subtract $1$ from $- 1$ .

$\frac{2 k - 2}{k ((k + 1) \cdot 0 + k - 1 - 1) - 1}$

Step 2.3

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

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Step 2.3.1

Factor $2$ out of $2 k$ .

$\frac{2 (k) - 2}{k ((k + 1) \cdot 0 + k - 1 - 1) - 1}$

Step 2.3.2

Factor $2$ out of $- 2$ .

$\frac{2 (k) + 2 (- 1)}{k ((k + 1) \cdot 0 + k - 1 - 1) - 1}$

Step 2.3.3

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

$\frac{2 (k - 1)}{k ((k + 1) \cdot 0 + k - 1 - 1) - 1}$

Step 3

Simplify the denominator.

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Step 3.1

Multiply $k + 1$ by $0$ .

$\frac{2 (k - 1)}{k (0 + k - 1 - 1) - 1}$

Step 3.2

Add $0$ and $k$ .

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

Step 3.3

Subtract $1$ from $- 1$ .

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

Step 3.4

Apply the distributive property.

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

Step 3.5

Multiply $k$ by $k$ .

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

Step 3.6

Move $- 2$ to the left of $k$ .

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