Question

Solve the following equation for r : (1/t(t-1)) - 1/t = 3/t-1

Answer 1

$Domain:\\\\t(t-1)\neq0\to t\neq0\ \vee\ t\neq1$

$\dfrac{1}{t(t-1)}-\dfrac{1}{t}=\dfrac{3}{t-1}\qquad|+\dfrac{1}{t}\\\\\dfrac{1}{t(t-1)}=\dfrac{3}{t-1}+\dfrac{1}{t}\\\\\dfrac{1}{t(t-1)}=\dfrac{(3)(t)}{t(t-1)}+\dfrac{(1)(t-1)}{t(t-1)}\\\\\dfrac{1}{t(t-1)}=\dfrac{3t+t-1}{t(t-1)}\\\\\dfrac{1}{t(t-1)}=\dfrac{4t-1}{t(t-1)}\iff1=4t-1\qquad|+1\\\\2=4t\to4t=2\qquad|:4\\\\\boxed{t=0.5}$