Question

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

Answer 1

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

Answer 2

x = ±√2

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.