Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $2$ .

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Step 1.1.1

Cancel the common factor.

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

Step 1.1.2

Divide $k$ by $1$ .

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

Step 1.2

Factor $5$ out of $5 k + 5$ .

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Step 1.2.1

Factor $5$ out of $5 k$ .

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

Step 1.2.2

Factor $5$ out of $5$ .

$k - \frac{5 (k) + 5 (1)}{2 k^{2} + 4 k}$

Step 1.2.3

Factor $5$ out of $5 (k) + 5 (1)$ .

$k - \frac{5 (k + 1)}{2 k^{2} + 4 k}$

Step 1.3

Factor $2 k$ out of $2 k^{2} + 4 k$ .

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Step 1.3.1

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

$k - \frac{5 (k + 1)}{2 k (k) + 4 k}$

Step 1.3.2

Factor $2 k$ out of $4 k$ .

$k - \frac{5 (k + 1)}{2 k (k) + 2 k (2)}$

Step 1.3.3

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

$k - \frac{5 (k + 1)}{2 k (k + 2)}$

Step 2

To write $k$ as a fraction with a common denominator, multiply by $\frac{2 k (k + 2)}{2 k (k + 2)}$ .

$k \cdot \frac{2 k (k + 2)}{2 k (k + 2)} - \frac{5 (k + 1)}{2 k (k + 2)}$

Step 3

Simplify terms.

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Step 3.1

Combine $k$ and $\frac{2 k (k + 2)}{2 k (k + 2)}$ .

$\frac{k (2 k (k + 2))}{2 k (k + 2)} - \frac{5 (k + 1)}{2 k (k + 2)}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{k (2 k (k + 2)) - 5 (k + 1)}{2 k (k + 2)}$

Step 4

Simplify the numerator.

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Step 4.1

Rewrite using the commutative property of multiplication.

$\frac{2 k (k (k + 2)) - 5 (k + 1)}{2 k (k + 2)}$

Step 4.2

Multiply $k$ by $k$ by adding the exponents.

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Step 4.2.1

Move $k$ .

$\frac{2 (k \cdot k) (k + 2) - 5 (k + 1)}{2 k (k + 2)}$

Step 4.2.2

Multiply $k$ by $k$ .

$\frac{2 k^{2} (k + 2) - 5 (k + 1)}{2 k (k + 2)}$

Step 4.3

Apply the distributive property.

$\frac{2 k^{2} k + 2 k^{2} \cdot 2 - 5 (k + 1)}{2 k (k + 2)}$

Step 4.4

Multiply $k^{2}$ by $k$ by adding the exponents.

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Step 4.4.1

Move $k$ .

$\frac{2 (k \cdot k^{2}) + 2 k^{2} \cdot 2 - 5 (k + 1)}{2 k (k + 2)}$

Step 4.4.2

Multiply $k$ by $k^{2}$ .

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Step 4.4.2.1

Raise $k$ to the power of $1$ .

$\frac{2 (k^{1} k^{2}) + 2 k^{2} \cdot 2 - 5 (k + 1)}{2 k (k + 2)}$

Step 4.4.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{2 k^{1 + 2} + 2 k^{2} \cdot 2 - 5 (k + 1)}{2 k (k + 2)}$

Step 4.4.3

Add $1$ and $2$ .

$\frac{2 k^{3} + 2 k^{2} \cdot 2 - 5 (k + 1)}{2 k (k + 2)}$

Step 4.5

Multiply $2$ by $2$ .

$\frac{2 k^{3} + 4 k^{2} - 5 (k + 1)}{2 k (k + 2)}$

Step 4.6

Apply the distributive property.

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

Step 4.7

Multiply $- 5$ by $1$ .

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