Question

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

Answer 1

`x=+-1`

Explanation:

Given: `" "(x^4-1)/x^3=0`

Multiply both sides by `x^3`

`(x^4-1)xx x^3/x^3 = 0xxx^3`

`x^4-1=0`

Add 1 to both sides

`x^4-1+1=0+1`

`x^4+0=1`

Take the 4th root of both sides

`root(4)(x)=root(4)(1)`

`color(red)(x=+-1)`
'~~~~~~~~~~~~~~~~~~~~~
Check:

`color(blue)("Suppose " x=-1)`

`" "((-1)^4-1)/((-1)^3)=0`

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

`color(blue)("Suppose " x=+1)`

`" "((+1)^4-1)/((+1)^3)=0`

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