Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.

Solve the following equation. Show all your work.

x
x

2
+
x

1
x
+
1
=

1

1 answer

To solve the equation:

1. Simplify the left side by finding a common denominator:
x(x-1) - 2(x+1) = -1(x+1)(x-1)
x^2 - x - 2x - 2 = -x^2 + x + x - 1
2x^2 - 4 = 0

2. Solve for x by factoring:
2(x^2 - 2) = 0
x^2 - 2 = 0
(x + √2)(x - √2) = 0
x = √2 or x = -√2

Therefore, the solution set is {√2, -√2}.