To solve for x in the equation x/(x-2) + (x-1)/(x+1) = -1, we need to find a common denominator and combine the fractions on the left side of the equation.
First, find a common denominator for (x-2) and (x+1). The common denominator is (x-2)(x+1).
So, we rewrite the equation as follows:
[(x(x+1) + (x-1)(x-2))/((x-2)(x+1))] = -1
Now, simplify the equation:
[(x^2 + x + x^2 - 3x + 2)/((x-2)(x+1))] = -1
[(2x^2 - 2x + 2)/((x-2)(x+1))] = -1
Now, multiply both sides of the equation by ((x-2)(x+1)) to eliminate the denominator:
2x^2 - 2x + 2 = -1
Rearrange the equation and set it equal to 0:
2x^2 - 2x + 2 + 1 = 0
2x^2 - 2x + 3 = 0
Now, this is a quadratic equation. We can use the quadratic formula to solve for x:
x = [-(-2) ± √((-2)^2 - 4(2)(3))] / 2(2)
x = [2 ± √(4 - 24)] / 4
x = [2 ± √(-20)] / 4
x = [2 ± 2√5i] / 4
x = (1 ± √5i) / 2
Therefore, the solutions for x are x = (1 + √5i)/2 and x = (1 - √5i)/2.
solve for x
x/x-2 + x-1/x+1 = -1
1 answer
1 answer