Precalculus Examples

$\frac{3}{- 4 k^{2} - 5 \sqrt{k^{4}}}$

Step 1

Simplify the denominator.

Tap for more steps...

Step 1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{k^{4}}$ as $k^{\frac{4}{2}}$ .

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

Step 1.2

Divide $4$ by $2$ .

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

Step 1.3

Subtract $5 k^{2}$ from $- 4 k^{2}$ .

$\frac{3}{- 9 k^{2}}$

Step 2

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 2.1

Cancel the common factor of $3$ and $- 9$ .

Tap for more steps...

Step 2.1.1

Factor $3$ out of $3$ .

$\frac{3 (1)}{- 9 k^{2}}$

Step 2.1.2

Cancel the common factors.

Tap for more steps...

Step 2.1.2.1

Factor $3$ out of $- 9 k^{2}$ .

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

Step 2.1.2.2

Cancel the common factor.

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

Step 2.1.2.3

Rewrite the expression.

$\frac{1}{- 3 k^{2}}$

Step 2.2

Move the negative in front of the fraction.

$- \frac{1}{3 k^{2}}$