Chapter 11 - Rational Expressions and Functions - 11-5 Solving Rational Equations - Practice and Problem-Solving Exercises - Page 695: 17

The equation has two solutions, -2 and 4.

$\frac{1}{t-2}=\frac{t}{8}$ $t(t-2)=8$ $t^2-2t=8$ $t^2-2t-1=9$ $(t-1)^2=9$ $t-1=3$ or $t-1=-3$ $t=4$ or $t=-2$ Check: $1/(4-2)=1/2;4/8=1/2$ $1/(-2-2)=-1/4;-2/8=-1/4$ The equation has two solutions, -2 and 4.