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

1 Answer
Tony B
Mar 6, 2016

#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")#

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