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Question
`1/(2a+b+2x)=1/(2a)+1/b+1/(2x)`
Solution
`1/(2a+b+2x)=1/(2a)+1/b+1/(2x)`
⇒`1/(2a+b+2x)=1/(2x)+1/b+1/(2x)`
⇒`(2x-2a-b-2x)/(2x(2a+b+2x))=(2a+b)/(2ab)`
⇒`( -(2a+b))/(4x^2+4ax+2bx)=(2a+b)/(2ab)`
⇒` 4x^2+4ax+2bx=-2ab`
⇒`4x^2+4ax+2bx+2ab=0`
⇒`4x(x+a)+2b(x+a)=0`
⇒`(x+a) (4x+2b)=0`
⇒`x+a=0 or 4x+2b=0`
⇒`x=-a or x=-b/2`
Hence,-a and `-b/2` are the roots of the give equation.
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