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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/(2a)+1/b+1/(2x)`
`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`
`rArrx=-a,` or `x=(-b)/2`
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