1/a+b+x=1/a+1/b+1/c solve the value of x
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1/(a+b+x)=1/a + 1/b +1/x
or, 1/(a+b+x)- 1/x =1/b+1/a
or,(x-a-b-x)/ax+bx+x^2=(a+b)/ab
or,-(a+b)/ax+bx+x^2=(a+b)/ab
or,x^2+ax+bx+ab=0
or, (x+a)(x+b)=0
therefore; x=(-a)or (-b)
or, 1/(a+b+x)- 1/x =1/b+1/a
or,(x-a-b-x)/ax+bx+x^2=(a+b)/ab
or,-(a+b)/ax+bx+x^2=(a+b)/ab
or,x^2+ax+bx+ab=0
or, (x+a)(x+b)=0
therefore; x=(-a)or (-b)
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x=-a,-b............................................
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