First, let's simplify the left side of the equation.
(xx) - 2 + x - 1/x + 1
x^2 - 2 + x - 1/x + 1
Next, let's combine like terms:
x^2 + x - 1/x - 1
Now, let's set the equation equal to -1:
x^2 + x - 1/x - 1 = -1
Now, we need to isolate x to solve for it. Let's move the -1 to the other side of the equation:
x^2 + x - 1/x - 1 + 1 = 0
x^2 + x - 1/x = 0
Now, we have a quadratic equation in terms of x. We can multiply through by x to clear the fraction:
x^3 + x^2 - 1 = 0
This equation can be factored by grouping:
(x^3 + x^2) - 1 = 0
x^2(x + 1) - 1 = 0
(x^2 - 1)(x + 1) = 0
(x + 1)(x + 1)(x - 1) = 0
Setting each factor equal to zero:
x + 1 = 0 --> x = -1
x - 1 = 0 --> x = 1
Therefore, the solutions to the equation are x = -1 and x = 1.
Solve the following equation. Show all your work.
xx−2+x−1x+1=−1
1 answer