Question 317234
1/(x-1)+1/x=1/3 find the LCM x(x-1).
(x+x-1)/x(x-1)=1/3 combine like terms.
(2x-1)/(x^2-x)=1/3 cross multiply.
x^2-x=3(2x-1)
x^2-x=6x-3
x^2-x-6x+3=0
x^2-7x+3=0
 {{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
x=(7+-sqrt[-7^2-4*1*3])/2*1
x=(7+-sqrt[49+12])/2
x=(7+-sqrt37)/2
x=(7+-6.08)/2
x=(7+6.08)/2
x=13.08/2
x=6.54 hrs. for the old machine.
6.54-1=5.54 hrs. for the newer machine.
Proof:
1/5.54+1/6.54=1/3
.181+.153=.333
.334~.333