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Solve for x :-
![\frac{1}{2a \: + \: b \: + \: 2x} = \: \frac{1}{2a} \: + \: \frac{1}{b} \: + \: \frac{1}{x} \frac{1}{2a \: + \: b \: + \: 2x} = \: \frac{1}{2a} \: + \: \frac{1}{b} \: + \: \frac{1}{x}](https://tex.z-dn.net/?f=+%5Cfrac%7B1%7D%7B2a+%5C%3A+%2B+%5C%3A+b+%5C%3A+%2B+%5C%3A+2x%7D+%3D+%5C%3A+%5Cfrac%7B1%7D%7B2a%7D+%5C%3A+%2B+%5C%3A+%5Cfrac%7B1%7D%7Bb%7D+%5C%3A+%2B+%5C%3A+%5Cfrac%7B1%7D%7Bx%7D+)
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May this will help you
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HridayAg0102:
great answer ☺☺☺☺
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1/(2a+b+2x)=1/2x +1/2a + 1/b
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
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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