Question from quadratic equation, find the value of x if 1/(2a+b+2x) = 1/2a+1/b+1/2x, x≠0

Question

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Solve for 'x' : 1/(2a+b+2x) = 1/2a+1/b+1/2x, x≠0

Answer 1

1/(2a+b+2x) - 1 / (2x) = 1 / 2a + 1 / b

(2x - 2a - b - 2x) / (2x)(2a+b+2x) = (2a + b) / 2ab

-(2a + b) / (2x)(2a+b+2x) = (2a + b) / 2ab

2a + b gets cancelled.

-2ab = (2x)(2a+b+2x)

-2ab = 4ax + 2bx + 4x²

4x2 + 2bx + 4ax + 2ab = 0

2x(2x + b) + 2a(2x + b) = 0

(2x +2a)(2x + b) = 0

2x + 2a = 0

x = - a

2x + b = 0

x = - b / 2

So, x = -a , -b/2