Question

One by Two a + b + 2 x is equal to 1 by 2a+ 1 by b + 1 by 2 x

Answer 1

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

[2a - (2a+b+2x)] / [2a(2a+b+2x)] = (b+2x) / [2bx]

-(2x+b) / [2a(2a+b+2x)] = (b+2x)/ (2bx)

-1 / [a(2a+b+2x)] = 1/(bx)

-bx = 2a2 + ab + 2ax

So, x = [a(2a+b)] / [-(b + 2a)]

So, x = -a

Answer 2

x = -b/2, -a

Step-by-step explanation:

Given,

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

To find,

x = ?

so,

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

by cancelling (2a + b), we get

⇒ -2ab = (2x) (2a+b+2x)

⇒ 2ab = 4ax + 2bx + 4x^2

⇒ 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

∵ x = -b/2 , -a

Learn more: find the value of x

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