Question:
Solution:
Consider the following equation:
[tex]x^3-3x^2-4=\frac{1}{x-1}+5[/tex]
this is equivalent to:
[tex]x^3-3x^2=\frac{1}{x-1}+5+4[/tex]
that is:
[tex]x^3-3x^2=\frac{1}{x-1}+9[/tex]
Multiplying both sides by (x-1), we obtain:
[tex](x-1)(x^3-3x^2)=1+9(x-1)[/tex]
this is equivalent to:
[tex](x-1)x^3-3x^2(x-1)=1+9(x-1)[/tex]
solving for x, we obtain that the correct solutions are:
[tex]x\text{ }\approx0.90672[/tex]
and
[tex]x\approx\: 3.68875[/tex]
