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

Apr 7, 2018

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

#### Explanation:

$\left(\frac{1}{x + 1}\right) - \frac{1}{x} = \frac{1}{2}$

$\frac{x - x - 1}{x \cdot \left(x + 1\right)} = \frac{1}{2} , \text{ taking L C M for L H S}$

$- 1 \cdot 2 = x \cdot \left(x + 1\right) , \text{ cross multiplying}$

${x}^{2} + x = - 2$

${x}^{2} + x + 2 = 0$

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

${x}_{+} = \frac{- 1 + \left(\sqrt{1 - 8}\right)}{2} = \frac{- 1 + i \sqrt{7}}{2}$

${x}_{-} = \frac{- 1 - \left(\sqrt{1 - 8}\right)}{2} = \frac{- 1 - i \sqrt{7}}{2}$