How do I use the quadratic formula to solve $1/(x+1) - 1/x = 1/2$ ?

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Answer 1 · 2018-04-07T03:44:51

$color(green)(x_+ = (-1 + isqrt7)/2, " " x_- = (-1 - isqrt7)/2$

$(1/(x+1)) - 1/x = 1/2$

$(x - x - 1) / (x * (x+1)) = 1/2, " taking L C M for L H S"$

$-1 * 2 = x * (x + 1), " cross multiplying"$

$x^2 + x = - 2$

$x^2 + x + 2 = 0$

![ www.biology.arizona.edu )

$"Applying the above formula with "$ a = 1, b = 1, c = 2 $" for finding the roots"$ ,

$x_+ = (-1 + (sqrt(1-8))) / 2 = (-1 + isqrt7)/2$

$x_- = (-1 - (sqrt(1-8))) / 2 = (-1 - isqrt7)/2$

How do I use the quadratic formula to solve 1/(x+1) - 1/x = 1/21/(x+1) - 1/x = 1/2?