Answer
The solutions are 1 and 10
Work Step by Step
$\frac{5}{x-6}$=$\frac{x}{x-2}$
(x-6)(x-2)$\frac{5}{x-6}$=(x-6)(x-2)$\frac{x}{x-2}$
$\frac{5}{x-6}$=$\frac{x}{x-2}$
(x-2)5=(x-6)x
5x-10=$x^{2}$-6x
0=$x^{2}$-6x-5x+10
0=$x^{2}$-11x+10
0=$x^{2}$-x-10x+10
0=x(x-1)-10(x-1)
0=(x-10)(x-1)
x-10=0 or x-1=0
x=10 or x=1
The solutions are 1 and 10
Check
Let x=1
$\frac{5}{x-6}$=$\frac{x}{x-2}$
$\frac{5}{1-6}$=$\frac{1}{1-2}$
$\frac{5}{-5}$=$\frac{1}{-1}$
-1=-1
Let x=10
$\frac{5}{x-6}$=$\frac{x}{x-2}$
$\frac{5}{10-6}$=$\frac{10}{10-2}$
$\frac{5}{4}$=$\frac{10}{8}$
$\frac{5}{4}$=$\frac{5}{4}$
