Answer
the solutions are -2 and 8
Work Step by Step
$\frac{t}{t-4}$=$\frac{t+4}{6}$
6(t-4)$\frac{t}{t-4}$=6(t-4)$\frac{(t+4)}{6}$
6t=$t^{2}$-16
0=$t^{2}$-6t-16
0=$t^{2}$+2t-8t-16
0=t(t+2)-8(t+2)
0=(t-8)(t+2)
t-8=0 or t+2=0
t=8 or t=-2
The solutions are -2 and 8
Check
Let t=-2
$\frac{t}{t-4}$=$\frac{t+4}{6}$
$\frac{-2}{-2-4}$=$\frac{-2+4}{6}$
$\frac{-2}{-6}$=$\frac{2}{6}$
$\frac{2}{6}$=$\frac{2}{6}$
Let t=8
$\frac{t}{t-4}$=$\frac{t+4}{6}$
$\frac{8}{8-4}$=$\frac{8+4}{6}$
$\frac{8}{4}$=$\frac{12}{6}$
2=2