Answer
-4 and 3
Work Step by Step
$\frac{a}{a-6}$=$\frac{-2}{a-1}$
(a-6)(a-1)[$\frac{a}{a-6}$]=(a-6)(a-1)$\frac{-2}{a-1}$
(a-1)a=-2(a-6)
$a^{2}$-a=-2a+12
$a^{2}$-a+2a-12=0
$a^{2}$+a-12=0
$a^{2}$-3a+4a-12=0
a(a-3)+4(a-3)=0
(a+4)(a-3)=0
a+4=0 or a-3=0
a=-4 or a=3
The solutions are -4 and 3
Check
Let a=3
$\frac{a}{a-6}$=$\frac{-2}{a-1}$
$\frac{3}{3-6}$=$\frac{-2}{3-1}$
$\frac{3}{-3}$=$\frac{-2}{2}$
-1=-1
Let a=-4
$\frac{a}{a-6}$=$\frac{-2}{a-1}$
$\frac{-4}{-4-6}$=$\frac{-2}{-4-1}$
$\frac{-4}{-10}$=$\frac{-2}{-5}$
$\frac{-2}{-5}$=$\frac{-2}{-5}$
