Question 102468
I think this is what you mean.
{{{1/x^3+4/x^2+4/x=0}}}
First step, get rid of any x expressions in the denominators by multiplying both sides by x^3.
{{{x^3*(1/x^3+4/x^2+4/x)=x^3*(0)}}}
{{{x^3*(1/x^3)+(4*x^3/x^2)+(4*x^3/x)=0}}}Distributive property
{{{1*x^(3-3)+4*x^(3-2)+4*x^(3-1)=0}}}Dividing same base, subtract exponents
{{{1+4x+4x^2=0}}} Simplify.
{{{4x^2+4x+1=0}}} A quadratic equation.
{{{x^2+x+1/4=0}}} Divide both sides by 4. 
{{{(x+1/2)^2=0}}} Factor the quadratic equation. 
{{{sqrt((x+1/2)^2)=0}}} Take the square root of both sides. 
{{{x+1/2=0}}}
{{{x=-1/2}}} 
Check your answer using the value for x and your original equation. 
{{{1/x^3+4/x^2+4/x=0}}}
{{{x^3=-1/8}}}
{{{highlight(1/x^3=-8)}}}
{{{x^2=1/4}}}
{{{1/x^2=4}}}
{{{highlight(4/x^2=16)}}}
{{{x=-1/2}}}
{{{1/x=-2}}}
{{{highlight(4/x=-8)}}}
Now plug those values into your original equation. 
{{{highlight(1/x^3)+highlight(4/x^2)+highlight(4/x)=0}}}
{{{-8+16-8=0}}}
{{{0=0}}}
Good answer.