Question

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

Answer 1

`Domain:\\\\t(t-1)\\eq0\to t\\eq0\ \vee\ t\\eq1`

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