I have that -5 is a solution to the problem (2x) / (x^2 -1) = (4x^2+6x-6) / (x^3+x^2-x-1) - (1) / x+1 but when I plug it in I dont get that's it the solution, but I know for a fact it is a solution. Can someone please show me how they plug it in so I see where aim going wrong. I think I'm not good at using order of operations.
Solve for x over the real numbers:
(2 x)/(x^2-1) = (4 x^2+6 x-6)/(x^3+x^2-x-1)-1/(x+1)
Multiply both sides by (x^2-1) (x+1):
2 x (x+1) = 1-x^2+2 (2 x^2+3 x-3)
Expand out terms of the left hand side:
2 x^2+2 x = 1-x^2+2 (2 x^2+3 x-3)
Expand out terms of the right hand side:
2 x^2+2 x = 3 x^2+6 x-5
Subtract 3 x^2+6 x-5 from both sides:
-x^2-4 x+5 = 0
The left hand side factors into a product with three terms:
-(x-1) (x+5) = 0
Multiply both sides by -1:
(x-1) (x+5) = 0
Split into two equations:
x-1 = 0 or x+5 = 0
Add 1 to both sides:
x = 1 or x+5 = 0
Subtract 5 from both sides:
x = 1 or x = -5
(2 x)/(x^2-1) ⇒ (2 (-5))/((-5)^2-1) = -5/12
(4 x^2+6 x-6)/(x^3+x^2-x-1)-1/(x+1) ⇒ (-6+6 (-5)+4 (-5)^2)/(-1--5+(-5)^2+(-5)^3)-1/(1-5) = -5/12:
So this solution is correct
(2 x)/(x^2-1) ⇒ 2/(1^2-1) = ∞^~
(4 x^2+6 x-6)/(x^3+x^2-x-1)-1/(x+1) ⇒ (-6+6 1+4 1^2)/(-1-1+1^2+1^3)-1/(1+1) = ∞^~:
So this solution is incorrect
The solution is:
Answer: |x = -5
