Question

y=b+a(t-1)/(t+1);solve for t

Answer 1

subtract b from both sides\[y-b=a\frac{t-1}{t+1}\]divide both sides by a\[\frac{y-b}{a}=\frac{t-1}{t+1}\]multiply by t+1\[(\frac{y-b}{a})(1+t)=t-1\]use Distributive Property for left side\[(\frac{y-b}{a})+(\frac{y-b}{a})t=t-1\]isolate the terms including t\[(\frac{y-b}{a})t-t=-1-(\frac{y-b}{a})\]factor out t from left side\[t((\frac{y-b}{a})-1)=-1-(\frac{y-b}{a})\]finally u have\[t=\frac{-1-(\frac{y-b}{a})}{(\frac{y-b}{a})-1}\]