Simplify (4-1/k)/(8/k-2/(k^2))

$\frac{4 - \frac{1}{k}}{\frac{8}{k} - \frac{2}{k^{2}}}$

Step 1

Multiply the numerator and denominator of the complex fraction by $k^{2}$ .

Multiply $\frac{4 - \frac{1}{k}}{\frac{8}{k} - \frac{2}{k^{2}}}$ by $\frac{k^{2}}{k^{2}}$ .

$\frac{k^{2}}{k^{2}} \cdot \frac{4 - \frac{1}{k}}{\frac{8}{k} - \frac{2}{k^{2}}}$

Combine.

$\frac{k^{2} (4 - \frac{1}{k})}{k^{2} (\frac{8}{k} - \frac{2}{k^{2}})}$

Step 2

Apply the distributive property.

$\frac{k^{2} \cdot 4 + k^{2} (- \frac{1}{k})}{k^{2} \frac{8}{k} + k^{2} (- \frac{2}{k^{2}})}$

Step 3

Simplify by cancelling.

Cancel the common factor of $k$ .

Move the leading negative in $- \frac{1}{k}$ into the numerator.

$\frac{k^{2} \cdot 4 + k^{2} \frac{- 1}{k}}{k^{2} \frac{8}{k} + k^{2} (- \frac{2}{k^{2}})}$

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

$\frac{k^{2} \cdot 4 + k \cdot k \frac{- 1}{k}}{k^{2} \frac{8}{k} + k^{2} (- \frac{2}{k^{2}})}$

Cancel the common factor.

$\frac{k^{2} \cdot 4 + k \cdot k \frac{- 1}{k}}{k^{2} \frac{8}{k} + k^{2} (- \frac{2}{k^{2}})}$

Rewrite the expression.

$\frac{k^{2} \cdot 4 + k \cdot - 1}{k^{2} \frac{8}{k} + k^{2} (- \frac{2}{k^{2}})}$

Cancel the common factor of $k$ .

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

$\frac{k^{2} \cdot 4 + k \cdot - 1}{k \cdot k \frac{8}{k} + k^{2} (- \frac{2}{k^{2}})}$

Cancel the common factor.

$\frac{k^{2} \cdot 4 + k \cdot - 1}{k \cdot k \frac{8}{k} + k^{2} (- \frac{2}{k^{2}})}$

Rewrite the expression.

$\frac{k^{2} \cdot 4 + k \cdot - 1}{k \cdot 8 + k^{2} (- \frac{2}{k^{2}})}$

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

Move the leading negative in $- \frac{2}{k^{2}}$ into the numerator.

$\frac{k^{2} \cdot 4 + k \cdot - 1}{k \cdot 8 + k^{2} \frac{- 2}{k^{2}}}$

Cancel the common factor.

$\frac{k^{2} \cdot 4 + k \cdot - 1}{k \cdot 8 + k^{2} \frac{- 2}{k^{2}}}$

Rewrite the expression.

$\frac{k^{2} \cdot 4 + k \cdot - 1}{k \cdot 8 - 2}$

Step 4

Simplify the numerator.

Factor $k$ out of $k^{2} \cdot 4 + k \cdot - 1$ .

Factor $k$ out of $k^{2} \cdot 4$ .

$\frac{k (k \cdot 4) + k \cdot - 1}{k \cdot 8 - 2}$

Factor $k$ out of $k \cdot - 1$ .

$\frac{k (k \cdot 4) + k (- 1)}{k \cdot 8 - 2}$

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

$\frac{k (k \cdot 4 - 1)}{k \cdot 8 - 2}$

Move $4$ to the left of $k$ .

$\frac{k (4 k - 1)}{k \cdot 8 - 2}$

Step 5

Simplify the denominator.

Factor $2$ out of $k \cdot 8 - 2$ .

Factor $2$ out of $k \cdot 8$ .

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

Factor $2$ out of $- 2$ .

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

Factor $2$ out of $2 (k \cdot 4) + 2 (- 1)$ .

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

Move $4$ to the left of $k$ .

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

Step 6

Cancel the common factor of $4 k - 1$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{k}{2}$

Simplify (4-1/k)/(8/k-2/(k^2))

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