Answer:
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.
