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

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Answer 1 · 2017-02-18T03:40:27

#x = 3#

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#