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Question

Solve for x
1a+b+x=1a+1b+1x,a+b0

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Solution

1a+b+x1x=1a+1bxabxx2+(a+b)x=a+bab(ab)x2+(a+b)x=a+bab1x2+(a+b)x=1abab=x2+(a+b)xx2+(a+b)x+ab=0x2+ax+bx+ab=0x(x+a)+b(x+a)=0(x+b)(x+a)=0x=b,a

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