Solve by factorisation (quadratic equations)

1/2a+b+2x = 1/2a+ 1/b +1/2x

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Solution

1/2a+b+2x = 1/2a+ 1/b +1/2x

=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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Similar questions

\frac{1}{2 a + b + 2 x} = \frac{1}{2 a} + \frac{1}{b} + \frac{1}{2 x}

\frac{1}{2 a + b + 2 x} = \frac{1}{2 a} + \frac{1}{b} + \frac{1}{2 x}

Solve for $x : \frac{1}{2 a + b + 2 x} = \frac{1}{2 a} + \frac{1}{b} + \frac{1}{2 x}$

\frac{1}{2 a + b + 2 x} = \frac{1}{2 a} . \frac{+ 1}{b} + \frac{1}{2 x}

2 x^{2} - 2 x + \frac{1}{2} = 0

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