Compute all values of x such that x-1 is the reciprocal of x+1. Express your answer in simplified radical form.

x = ±√2

Step-by-step explanation:

x - 1 = 1 / (x + 1)

(x - 1) (x + 1) = 1 Multiplied each side by x + 1

x² - 1 = 1 Difference of two squares

x² = 2 Add 1 to each side

x = ±√2

x-1 is the reciprocal of x+1 when x = - √2 or x = √2.

Check:

(a) x = - √2

-√2 - 1 = 1 / (-√2 + 1)

- (√2 + 1) = (√2 + 1) / [ (-√2 + 1) (√2 + 1) ]

- (√2 + 1) = (√2 + 1) / (-2 + 1)

- (√2 + 1) = (√2 + 1) / (-1)

- (√2 + 1) = - (√2 + 1)

(b) x = √2

√2 - 1 = 1 / (√2 + 1

√2 - 1 = (√2 - 1) / [ (√2 + 1) (√2 - 1) ]

√2 - 1 = (√2 - 1) / (2 - 1)

√2 - 1 = (√2 - 1) / 1

√2 - 1 = √2 - 1

OK.

Answer:x = ±√2

Step-by-step explanation: this is because reciprocal means the numerator and denominator switches

So the equation is x-1=1 / (x+1)

And you solve for it thats how u get the answer