1/a+b+x=bx+ax+ab/abx
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a+b+x
1
=
a
1
+
b
1
+
x
1
⟹
a+b+x
1
=
abx
bx+ax+ab
⟹abx=abx+a
2
x+a
2
b+b
2
x+abx+ab
2
+bx
2
+ax
2
+abx
⟹x
2
(a+b)+x(2ab+a
2
+b
2
)+(a
2
b+ab
2
)=0
⟹x
2
(a+b)+x(a+b)
2
+ab(a+b)=0
⟹x
2
+x(a+b)+ab=0
⟹x
2
+ax+bx+ab=0
⟹(x+a)(x+b)=0
∴x=−a, x=−b
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