Expert: Lynn Houston - 10/22/2009

Question
QUESTION: solve for X.
3+1/x+1 = 4x/x-1

solve the inequality
2x²-x>6

ANSWER: solve for X.
3+1/(x+1) = 4x/(x-1) (multiply both sides by (x+1)(x-1)
(3+1)(x-1) = 4x(x+1) Multiply
3x + x - 3 - 1 = 4x^2 + 4x  set = to 0
4x^2 + 4x -3x - x +4 = 0 combine like terms
4x^2 + 4 = 0
4(x^2 + 1) = 0

If I have the parentheses correct, then x = i^2 or i^-2


solve the inequality
2x²-x>6
2x²-x- 6 >0
(2x+3)(x-2)> 0
x < -3/2 or x>2

---------- FOLLOW-UP ----------

QUESTION: Do we multiply (x+1) (x-1) by 3 and then 1/x+1 by (x+1) (x-1) for the part on the left. please help am confused.
Thank you so so much.

Answer
I meant, both sides of the eq, meaning, the part to the right of the = sign and the part to the left.  The part I skipped would look like this


(3+1)(x+1)(x-1)/(x+1) = 4x(x+1)(x-1)/(x-1)

You do this to get rid of the fractions (that's why it's (x+1) (x-1), that is the lowest common denominator).  You'll notice on the left side, the x+1 cancels out and on the right, the x-1 cancels out, leaving (3+1)(x-1) = 4x(x+1)