(x/x-2)+(x-1/x+1)=-1
So far I was able to get it to x + (x-1) = -(x-2)(x+1) through cross multiplying, but I'm kinda lost with what to do now. Should I convert the right side to a polynomial and add the left side, then bring it all to 1 side so it = 0?
Thanks!
yes
Thanks. My problem from there is figuring out how to factor it.. I have x^2+x-3=0. Theres no factors of -3 that add up to 1.
-3+1 = -2
-1+3= 2
When i try to use the quadratic formula I end up with: (-1+/1(sqrt)13)/2
Am I missing something?
Totally incorrect.
First of all, I think you meant:
(x/(x-2))+((x-1)/(x+1)) = -1
then,
(x(x+1) + (x-1)(x-2) )/((x-2)(x+1) ) = -1
x^2 + x + x^2 - 3x + 2 = -x^2 + x +
2
3x^2 - 3x = 0
3x(x-1)=0
x=0 or x = 1
verification:
https://www.wolframalpha.com/input/?i=solve+(x%2F(x-2))%2B((x-1)%2F(x%2B1))%3D-1
Ahhh! That makes a lot more sense, thanks for the breakdown. I knew I was doing SOMETHING wrong haha. Thanks again :D
To solve the equation (x/x-2) + (x-1/x+1) = -1, you're on the right track with cross multiplying to obtain x + (x-1) = -(x-2)(x+1). However, let's go through the steps to solve it from here.
1. Simplify the equation:
Combine like terms on both sides of the equation.
2x - 1 = -(x^2 - x - 2x - 2)
2. Expand and rearrange the equation:
Distribute the negative sign on the right side.
2x - 1 = -(x^2 - 3x - 2)
3. Distribute the negative sign again:
Now, distribute the negative sign within the parentheses on the right side.
2x - 1 = -x^2 + 3x + 2
4. Bring all terms to one side to form a quadratic equation:
Rearrange the equation to have all terms on the same side, making sure the equation is set equal to zero.
x^2 - 5x - 3 = 0
5. Solve the quadratic equation:
Now, you can either factor the quadratic equation or use the quadratic formula to find the values of x. In this case, the quadratic equation doesn't factor easily, so we'll use the quadratic formula.
x = (-b ± √(b^2 - 4ac)) / (2a)
In the quadratic equation x^2 - 5x - 3 = 0:
a = 1, b = -5, and c = -3
Substituting these values into the quadratic formula:
x = (-(-5) ± √((-5)^2 - 4(1)(-3))) / (2(1))
Simplifying,
x = (5 ± √(25 + 12)) / 2
x = (5 ± √37) / 2
So, the solutions to the equation (x/x-2) + (x-1/x+1) = -1 are x = (5 + √37) / 2 and x = (5 - √37) / 2.