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

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Answer 1 · 2018-06-05T18:53:31

#(3x)/(3x^5-4)#

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:
#(3x^0)/(3x^4-4x^-1)#
=#(3x)/(3x^4*x-4x^-1*x)#
=#(3x^0*x)/(3x^5-4)#
=#(3x)/(3x^5-4)#

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

Answer 2 · 2018-06-05T19:08:14

#(3x)/(3x^5-4)#

#(3x^0)/(3x^4-4x^-1)#

#:.=3/(3x^4-4x^-1)#

#:.=3/(x^-1(3x^5-4))#

#:.=(3x)/(3x^5-4)#