Answer
a. Restriction values $: 1 $
b. Solution set $ :\{3\}$
Work Step by Step
$\frac{1}{x-1} +5 = \frac{11}{x-1}$
a. $x = 1 $ makes the denominator zero. So, $x \ne 1$
b. $\frac{1}{x-1} +5 = \frac{11}{x-1}; x \ne 1;$
$\frac{1+5(x-1)}{x-1} = \frac{11}{x-1}; x \ne 1;$
$\frac{1+5x-5}{x-1} = \frac{11}{x-1}; x \ne 1;$
$\frac{5x-4}{x-1} = \frac{11}{x-1}; x \ne 1;$
Multiply both sides by $(x-1)$ to clear fraction.
$(x-1)(\frac{5x-4}{x-1} )= (x-1)(\frac{11}{x-1});$
$5x-4 = 11$
$5x = 11 +4$
$5x = 15$
Divide both sides by $5$
$x = 3$
