Part I

Given the following two rational expressions

1 / (x² - 1 ) , 1 / (x - 1)²

i. Determine the least common denominator (LCD) of the two expressions

ii. Expand each rational expression to its equivalent form having the LCD as its denominator

iii. Add the two resulting rational expressions, simplify if possible, and determine the domain of the resulting rational expression

Part II

For the quadratic equation

x² + x - 1 = 0.

i. Use the technique as specified in this lecture under the section Completing the Square to Determine the solutions (roots) of the equation

ii. Verify each root by plugging the root back into the equation and performing the computation