How do you solve (x - 3) /x = (x - 3) / (x - 6) ?

1 Answer
Feb 18, 2017

x = 3

Explanation:

Put the equation in y=0 form:

y = (x-3)/x = (x-3)/(x-6)

y = (x-3)/x - (x-3)/(x-6) = 0

Find a common denominator:
y = (x-3)/x * (x-6)/(x-6) - (x-3)/(x-6) * x/x= 0

Combine under the same denominator:

y = ((x-3)(x-6) - x(x-3))/(x(x-6)) = 0

Factor the numerator: (x-3)(x-6-x) = -6(x-3)

y = (-6(x-3))/(x(x-6)) = 0

The numerator gives a a solution when y = 0, when x = 3