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put this solution on YOUR website!Well first you need to get a common denominator. Since 2/3 of the fractions have a denominator of x-1 that will be your common denominator. So multiply everything by x-1 and the denominator cancles off leaving you with.
x+x(x-1)=4x-3
now just solve:
x+x(x-1)=4x-3 --> Distribute the x
x + x^2 - x = 4x - 3 --> Collect like terms on left hand side
x^2 - 4x + 3 = 0 --> Factor
(x-1)(x-3) = 0 --> Set each factor equal to zero and solve
x = 1 and x = 3
Now lets check our solutions
x/x-1 + x = 4x-3/x-1
when x = 1 you get
1/1-1 + 1 = 4-3/1-1 well since you can't divide by zero we know that x = 1 is a extraneous answer.
when x = 3 you get
3/3-1 + 3 = 4(3)-3/3-1
3/2 + 3 = 12-3/2
3/2 + 3 = 9/2
9/2 = 9/2
that one checks out.
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