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Question

Solve for x:1a+b+x=1a+1b+1x,[a,b,x0,x(a+b)]

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Solution

1a+b+x1x=1a+1b

xabxx(a+b+x)=a+bab

1x(a+b+x)=1ab

ab=ax+bx+x2

x2+(a+b)x+ab=0

x(x+a)(x+b)=0

x+a=0,x+b=0

x=a,b

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