Question

Solve the following inequalities
$f^{\prime }\left(x\right)>g^{\prime }\left(x\right)iff\left(x\right)=x+ln(x-5),g\left(x\right)=ln(x-1)$

Answer 1

$f^{\prime }\left(x\right)>g^{\prime }\left(x\right)$

$1+\frac{1}{x-5}>\frac{1}{x-1}$

$(x-4)(x-1)>x-5$

$x^2-6x+9>0$

$(x-3{)}^2>0$

So the solution set of the given inequality is $R-[-3,3]$