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

1 Answer
sankarankalyanam
Apr 7, 2018

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

Explanation:

#(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#

http://www.biology.arizona.edu/biomath/tutorials/quadratic/roots.html

#"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#

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