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Question
Solve the following for x:
`1/(2a+b+2x)=1/(2a)+1/b+1/(2x)`
Solution
The given equation is.`1/(2a+b+2x)=1/(2a)+1/b+1/(2x)`
`1/(2a+b+2x)=1/(2a)+1/b+1/(2x)`
`rArr1/(2a+b+2x)=1/(2x)=1/(2a)+1/b`
`rArr(2x-2a-b-2x)/(2x(2a+b+2x))=(b+2a)/(2ab)`
`rArr(-2a-b)/(2x(2a+b+2x))=(b+2a)/(2ab)`
`rArr(-(2a+b))/(2x(2a+b+2x))=(b+2a)/(2ab)`
`rArr(-1)/(2x(2a+b+2x))=(1)/(ab)`
`rArr 2x^2+2ax+bx+ab=0`
`rArr2x(x+a)+b(x+a)=0`
`rArr(x+a)(2x+b)=0`
`rArrx+a=0` or `2x+b=0`
`rArr x=-a` or `x=-b/2`
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