SOLUTION: x+3 over x^2-1 minus 2x over x-1 = 1

Question 1029931: x+3 over x^2-1 minus 2x over x-1 = 1
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
(x+3)/(x^2-1) - 2x/(x-1)=1
multiply everything by (x^2-1), the common denominator. The first term will be (x+3), because it is already divided by x^2-1. The second term is multiplied by (x+1), because x^2-1 =(x+1) (x-1). By multiplying the term by x^2-1, the (x-1) disappears, but the term is multiplied by (x+1), making the second term minus 2x(x+1), and the right side is just x^2-1
x+3-2x(x+1)=x^2-1. x^2-1 is the common denominator.
Distribute
x+3-2x^2-2x=x^2-1 after distributing
0=3x^2+x-4; move 2x^2 to the right, combine x and -2x to get -x, and move it to the right, move the 3 to the right as -3..
now 3x^2+x-4, after combining terms.
This equals 0
One may factor it into (3x+4)(x-1)=0
Set each term = to 0, and 3x+4=0, x=-4/3; x-1=0, x=1.
x=(-4/3),1. But 1 is extraneous.
x=-4/3
check
5/3/7/9 minus -8/3/7/3=45/21-8/7=45/21-24/21=1

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