Basic Math Examples

$\frac{k}{k - 5} + \frac{k}{k + 5}$

Step 1

To write $\frac{k}{k - 5}$ as a fraction with a common denominator, multiply by $\frac{k + 5}{k + 5}$ .

$\frac{k}{k - 5} \cdot \frac{k + 5}{k + 5} + \frac{k}{k + 5}$

Step 2

To write $\frac{k}{k + 5}$ as a fraction with a common denominator, multiply by $\frac{k - 5}{k - 5}$ .

$\frac{k}{k - 5} \cdot \frac{k + 5}{k + 5} + \frac{k}{k + 5} \cdot \frac{k - 5}{k - 5}$

Step 3

Write each expression with a common denominator of $(k - 5) (k + 5)$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{k}{k - 5}$ by $\frac{k + 5}{k + 5}$ .

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

Step 3.2

Multiply $\frac{k}{k + 5}$ by $\frac{k - 5}{k - 5}$ .

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

Step 3.3

Reorder the factors of $(k - 5) (k + 5)$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

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Step 5.1

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

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

Step 5.2

Add $k$ and $k$ .

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

Step 5.3

Subtract $5$ from $5$ .

$\frac{k (2 k + 0)}{(k + 5) (k - 5)}$

Step 5.4

Add $2 k$ and $0$ .

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

Step 5.5

Combine exponents.

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Step 5.5.1

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

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

Step 5.5.2

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

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

Step 5.5.3

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

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

Step 5.5.4

Add $1$ and $1$ .

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