Pre-Algebra Examples

$\frac{\frac{\frac{k + 1}{18 k}}{5 k - 1}}{6 k}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{\frac{k + 1}{18 k}}{5 k - 1} \cdot \frac{1}{6 k}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{k + 1}{18 k} \cdot \frac{1}{5 k - 1} \frac{1}{6 k}$

Step 3

Multiply $\frac{k + 1}{18 k}$ by $\frac{1}{5 k - 1}$ .

$\frac{k + 1}{18 k (5 k - 1)} \cdot \frac{1}{6 k}$

Step 4

Multiply $\frac{k + 1}{18 k (5 k - 1)} \cdot \frac{1}{6 k}$ .

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Step 4.1

Multiply $\frac{k + 1}{18 k (5 k - 1)}$ by $\frac{1}{6 k}$ .

$\frac{k + 1}{18 k (5 k - 1) (6 k)}$

Step 4.2

Multiply $6$ by $18$ .

$\frac{k + 1}{108 k (5 k - 1) k}$

Step 4.3

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

$\frac{k + 1}{108 (k^{1} k) (5 k - 1)}$

Step 4.4

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

$\frac{k + 1}{108 (k^{1} k^{1}) (5 k - 1)}$

Step 4.5

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

$\frac{k + 1}{108 k^{1 + 1} (5 k - 1)}$

Step 4.6

Add $1$ and $1$ .

$\frac{k + 1}{108 k^{2} (5 k - 1)}$

Step 5

Split the fraction $\frac{k + 1}{108 k^{2} (5 k - 1)}$ into two fractions.

$\frac{k}{108 k^{2} (5 k - 1)} + \frac{1}{108 k^{2} (5 k - 1)}$

Step 6

Cancel the common factor of $k$ and $k^{2}$ .

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Step 6.1

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

$\frac{k^{1}}{108 k^{2} (5 k - 1)} + \frac{1}{108 k^{2} (5 k - 1)}$

Step 6.2

Factor $k$ out of $k^{1}$ .

$\frac{k \cdot 1}{108 k^{2} (5 k - 1)} + \frac{1}{108 k^{2} (5 k - 1)}$

Step 6.3

Cancel the common factors.

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Step 6.3.1

Factor $k$ out of $108 k^{2} (5 k - 1)$ .

$\frac{k \cdot 1}{k (108 k (5 k - 1))} + \frac{1}{108 k^{2} (5 k - 1)}$

Step 6.3.2

Cancel the common factor.

$\frac{k \cdot 1}{k (108 k (5 k - 1))} + \frac{1}{108 k^{2} (5 k - 1)}$

Step 6.3.3

Rewrite the expression.

$\frac{1}{108 k (5 k - 1)} + \frac{1}{108 k^{2} (5 k - 1)}$