# How do you simplify \frac { 3x ^ { 0} } { 3x ^ { 4} - 4x ^ { - 1} }?

Jun 5, 2018

$\frac{3 x}{3 {x}^{5} - 4}$

#### Explanation:

Remember that ${x}^{o} = 1$
Multiply numerator and denominator with x to get rid of ${x}^{-} 1$ in the denominator.

If we do this, we get:
$\frac{3 {x}^{0}}{3 {x}^{4} - 4 {x}^{-} 1}$
=$\frac{3 x}{3 {x}^{4} \cdot x - 4 {x}^{-} 1 \cdot x}$
=$\frac{3 {x}^{0} \cdot x}{3 {x}^{5} - 4}$
=$\frac{3 x}{3 {x}^{5} - 4}$

I cannot see that it can be made much simpler than this.

Jun 5, 2018

$\frac{3 x}{3 {x}^{5} - 4}$

#### Explanation:

$\frac{3 {x}^{0}}{3 {x}^{4} - 4 {x}^{-} 1}$

$\therefore = \frac{3}{3 {x}^{4} - 4 {x}^{-} 1}$

$\therefore = \frac{3}{{x}^{-} 1 \left(3 {x}^{5} - 4\right)}$

$\therefore = \frac{3 x}{3 {x}^{5} - 4}$