Question

1/2a+b+x=1/2a+1/b+1/2x, 2a+b not equal to 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
Ans: x = -a , -b/2

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