# How do you solve ((x^4)-1)/(x^3)=0?

Mar 6, 2016

$x = \pm 1$

#### Explanation:

Given: $\text{ } \frac{{x}^{4} - 1}{x} ^ 3 = 0$

Multiply both sides by ${x}^{3}$

$\left({x}^{4} - 1\right) \times {x}^{3} / {x}^{3} = 0 \times {x}^{3}$

${x}^{4} - 1 = 0$

${x}^{4} - 1 + 1 = 0 + 1$

${x}^{4} + 0 = 1$

Take the 4th root of both sides

$\sqrt[4]{x} = \sqrt[4]{1}$

$\textcolor{red}{x = \pm 1}$
'~~~~~~~~~~~~~~~~~~~~~
Check:

$\textcolor{b l u e}{\text{Suppose } x = - 1}$

$\text{ } \frac{{\left(- 1\right)}^{4} - 1}{{\left(- 1\right)}^{3}} = 0$

0/(-1)=0" "color(red)("True")

$\textcolor{b l u e}{\text{Suppose } x = + 1}$

$\text{ } \frac{{\left(+ 1\right)}^{4} - 1}{{\left(+ 1\right)}^{3}} = 0$

0/(+1)=0" "color(red)("True")