Question 792379

Hello, my name is Eboni.

Solving Equation.
 
x-3/4x-4 +1/9= x-5/6x-6


It it's {{{(x - 3)/(4x - 4) + 1/9 = (x - 5)/(6x - 6)}}}, then read on.


Note that {{{x <> 1}}}


Denominators (4x - 4) and (6x - 6) factor to 4(x - 1) and 6(x - 1), respectively. Along with 9, we have denominators, 4(6)(9)(x - 1), which makes the LCD: 36(x - 1)


Therefore, {{{(x - 3)/(4x - 4) + 1/9 = (x - 5)/(6x - 6)}}} becomes: 


9(x - 3) + 4(x - 1) = 6(x - 5)


9x - 27 + 4x - 4 = 6x - 30


9x + 4x - 27 - 4 = 6x - 30 


13x - 31 = 6x - 30


13x - 6x = - 30 + 31


7x = 1


{{{highlight_green(x = 1/7)}}}


You can do the check!! 


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