I would be inclined to start like this. Keeping in mind thatQuestion:
I'm guessing I have to get rid of the fractions by multiplying by the LCD, but I feel like I am missing a step in even getting that.
You have two denominators: x - 1 and 1 - x2 = (1 - x)(1 + x). With a "minus" sign, the first denominator becomes -(1 - x). Take the "minus" sign through the numerator, and you get a subtraction on top.
You're right. It should go:
Can I cancel out both (x-1)'s and (3x-1)'s at this point?
Would 2(1-x) be the wrong answer?