SOLUTION: Hello the section im working on is on solving rational equations. I dont understand this one im working on. Here it is x/x-1 + x = 4x-3/x-1 Thanks for the help

Question 133919: Hello the section im working on is on solving rational equations. I dont understand this one im working on.
Here it is
x/x-1 + x = 4x-3/x-1
Thanks for the help
Answer by algebrapro18(249) (Show Source): You can 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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