Solve the following equation. Show all steps.
x/x-2+x-1/x+1=-1
I guess maybe you mean:
x/(x-2) + (x-1)/(x+1) = -1
multiply everything by
(x-2)(x+1)
x(x+1) + (x-1)(x-2) =-(x-2)(x+1)
x^2 + x +x^2 -3x +2 = -[ x^2-x-2 ]
2 x^2 -2x +2 = -x^2 + x + 2
3 x^2 - 3 x = 0
3 x (x-1) = 0
x = 0 or x = 1
Thank you so much!!
You are welcome.
To solve the equation (x/(x - 2)) + ((x - 1)/(x + 1)) = -1, we need to find the value of x that satisfies the equation.
Step 1: Clear the denominators by multiplying through by the common denominator, which is (x - 2)(x + 1).
(x/(x - 2)) * (x - 2)(x + 1) + ((x - 1)/(x + 1)) * (x - 2)(x + 1) = -1 * (x - 2)(x + 1)
Simplifying this equation further, we have:
x(x + 1) + (x - 1)(x - 2) = -1(x - 2)(x + 1)
Step 2: Expand and simplify both sides of the equation.
x^2 + x + (x - 1)(x - 2) = -x^2 + 3x - 2
x^2 + x + (x^2 - 3x + 2) = -x^2 + 3x - 2
Simplifying further, we have:
x^2 + x + x^2 - 3x + 2 = -x^2 + 3x - 2
Step 3: Combine like terms on both sides of the equation.
2x^2 - 2x + 2 = -x^2 + 3x - 2
Step 4: Move all terms to one side of the equation to solve for x.
2x^2 - 2x + x^2 - 3x + 3x + 2 - 2 = 0
Simplifying further, we have:
3x^2 - 2x = 0
Step 5: Factor out the common term x.
x(3x - 2) = 0
Step 6: Set each factor equal to zero and solve for x.
x = 0 or 3x - 2 = 0
Step 7: Solve for x in the second equation.
3x - 2 = 0
3x = 2
x = 2/3
Therefore, the two solutions to the equation are x = 0 and x = 2/3.